For the complex number z = 12 + i, what is Modifying above z with bar?

The total area of the given composite figure found using the areas of right triangles and rectangle is 231.68sq. yards.

What is a composite figure?

Composite geometric figures are made from two or more geometric figures. Finding the area of a composite shape can be done using one of two broad approaches.

The given composite figure consists of two right triangles and a rectangle.

The area of the figure is the sum of the areas of the right triangles and the rectangle.

Both the right triangle are the same.

So the area of one triangle = 0.5 * base * height = 0.5 * 6.4 * 12.8

                                                                = 40.96 sq. yards

So the total area of both triangles = 2 * 40.96 = 81.92 sq. yards.

Now the area of the rectangle = length * breadth = 14.9 * 12.8

                                                            = 190.72 sq. yards

The total area of the figure = 190.72+40.96 = 231.68 sq. yards.

Therefore the total area of the given composite figure found using the areas of right triangles and rectangle is 231.68sq. yards.

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We can deduce from these findings that the actual population mean is variable probably lower and reject the null hypothesis that the population mean for body temperature is 98.6o.

In the context of a mathematical idea or experiment, a variable is something that can be altered. Frequently, a single symbol is used to symbolize a variable. Variables are frequently represented by the letters x, y, and z as abstract symbols.

The first thing I want to say is that it is a widespread misconception that the average body temperature is 98.6 degrees. Although the "normal" or average body temperature is frequently stated as 98.6 degrees Fahrenheit (or 37 degrees Celsius), this value is not true for everyone. The average body temperature may actually be lower than previously thought, hovering around 97.5–97.7 degrees Fahrenheit, according to study.

Here is the SPSS output for the one-sample t-test so that we can get back to the job at hand:

Descriptive Statistics

N       Mean      Std. Deviation   Std. Error Mean

25      97.528    0.694            0.139

One-Sample Test

Test Value = 98.6

t         df        Sig. (2-tailed)   Mean Difference

-5.238    24        .000              -1.072

We can deduce from these findings that the actual population mean is probably lower and reject the null hypothesis that the population mean for body temperature is 98.6o.

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The equation 10 sin(4t) - 9 cos(4t) can be written in the form of A sin (Bt + C) as 10 sin (4t + C).

10 sin(4t) - 9 cos(4t) can be written in the form of A sin (Bt + C) as follows: A sin (Bt + C) = 10 sin(4t) - 9 cos(4t) = 10 sin (4t) - 9 (cos(4t) cos 0 - sin(4t) sin 0) = 10 sin (4t) + 9 sin (0) = 10 sin (4t) + 9 (0) = 10 sin (4t + 0) = 10 sin (4t + C) where A = 10 and B = 4. Thus, 10 sin (4t) - 9 cos (4t) can be written in the form of A sin (Bt + C) as 10 sin (4t + C).

To explain this in further detail, the trigonometric identities sin(A + B) = sin A cos B + cos A sin B and cos(A + B) = cos A cos B - sin A sin B can be used to rewrite the equation in the required form. To do this, set A = 4t and B = 0, then substitute A and B into the identities to get 10 sin (4t) - 9 cos (4t) = 10 sin (4t + 0) = 10 sin (4t + C). Therefore, the equation 10 sin(4t) - 9 cos(4t) can be written in the form of A sin (Bt + C) as 10 sin (4t + C).

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Yes, it is possible for the total distance travelled by the ball to be 35m.

Yes, it is possible for the total distance travelled by the ball to be 35m. This can happen in several ways. The ball can move in a straight line to cover a total distance of 35m. It can also move in a zigzag pattern, with the total distance covered still being 35m. Furthermore, the ball could move in a circular motion and cover a total distance of 35m. The ball could also travel in a number of different directions and still cover a total distance of 35m. In conclusion, it is possible for the total distance travelled by the ball to be 35m regardless of the path it takes.

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Answer:

100 times

Step-by-step explanation:

It is predicted that a 1 or a 6 will be rolled 50 times in 150 rolls of a standard number cube.

A standard number cube has six faces, each numbered from 1 to 6.

The probability of rolling a 1 or a 6 on any given roll is,

P = 2/6

P = 1/3

Since, there are two favorable outcomes out of six possible outcomes.

Hence, To predict how many times a 1 or a 6 will be rolled in 150 rolls, we can use the formula:

Number of times = Probability x Total number of rolls

So, the number of times a 1 or a 6 is expected to be rolled in 150 rolls is:

Number of times = (1/3) x 150 = 50

Therefore, it is predicted that a 1 or a 6 will be rolled approximately 50 times in 150 rolls of a standard number cube.

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Answer:

6 students

Step-by-step explanation:

We know

There are 120 students in the seventh grade.  5% are in the Environmental Club.

How many students are in the Environmental Club?

5% = 0.05

120 x 0.05 = 6 students

So, there are 6 students in the Environmental Club.

Answer:

6

Step-by-step explanation:

To find the answer to this question we have to find 5% of 120, this will give us how many students there are in the Environmental Club.

To do this we have to do...

Then...

This means that 6 of the students in the seventh grade are in the Environmental Club!

Hope this helps, have a lovely day! :)

Answer:2.6

Step-by-step explanation:

in order to find median you should sort your numbers first.

so our sorted numbers would be,

0.4  0.9  1.1  1.1  2.6  2.7  3.5  5.7  9.8

find middle element,

0.4  0.9  1.1  1.1  2.6 2.7  3.5  5.7  9.8

2.6 is median

The base 10 representatiοn οf the number 1406 (3 at the bοttοm) is 118.

In mathematics, a base number refers tο the number system used tο represent numeric values. The base number determines the number οf symbοls used tο represent each value, as well as the value οf each symbοl. The mοst cοmmοn base number systems are base 10 (decimal), base 2 (binary), base 8 (οctal), and base 16 (hexadecimal).

In base 10, we use 10 digits (0-9) tο represent all pοssible values. In binary, we use οnly twο digits (0 and 1) tο represent values. In οctal, we use eight digits (0-7), and in hexadecimal, we use 16 digits (0-9 and A-F) tο represent values.

Fοr example, the decimal number 125 can be represented in base 2 as 1111101, in base 8 as 175, and in base 16 as 7D.

Cοnverting a number frοm οne base tο anοther invοlves dividing the number by the base and repeatedly finding the remainder until the quοtient becοmes zerο. The remainders, read frοm bοttοm tο tοp, represent the digits οf the new number in the new base.

Tο cοnvert a number in base 3 tο base 10, we need tο multiply each digit οf the number by the cοrrespοnding pοwer οf 3, and then sum up the prοducts.

Starting frοm the rightmοst digit οf the number, the pοwers οf 3 increase by 1 fοr each digit tο the left. Sο, fοr the number 1406 (3 at the bοttοm), we have:

1 × 3⁰ + 0 × 3¹ + 4 × 3² + 1 × 3³ = 1 + 0 + 36 + 81 = 118

Therefοre, the base 10 representatiοn οf the number 1406 (3 at the bοttοm) is 118.

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The mean self-esteem score after the program (M = 43) is not significantly different from the population mean self-esteem score (μ0 = 40) at the α = 0.05 level.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain.

a. The null hypothesis (H0) is that the new physical education program has no effect on the self-esteem scores of elementary school children, or in other words, the mean self-esteem score after the program (μ) is equal to the population mean self-esteem score (μ0): H0: μ = μ0 = 40.

The alternative hypothesis (Ha) is that the new program has an effect on the self-esteem scores, either positive or negative, or in other words, the mean self-esteem score after the program (μ) is not equal to the population mean self-esteem score (μ0): Ha: μ ≠ μ0.

b.

Step 1: Set up the hypothesis:

H0: μ = μ0 = 40

Ha: μ ≠ μ0

Step 2: Determine the significance level: α = 0.05

Step 3: Calculate the test statistic:

z = (M - μ0) / (σ / sqrt(n))

z = (43 - 40) / (8 / sqrt(36))

z = 1.5

Step 4: Determine the critical value or p-value:

For a two-tailed test with α = 0.05, the critical values are -1.96 and 1.96.

Since the calculated test statistic (z = 1.5) is not in the rejection region (it falls between -1.96 and 1.96), we fail to reject the null hypothesis.

Alternatively, we can calculate the p-value using a standard normal distribution table or a calculator. The p-value for a two-tailed test with z = 1.5 is 0.134. Since the p-value is greater than the significance level (p > α), we fail to reject the null hypothesis.

Cohen's d can be calculated as d = (M - μ0) / s, where s is the standard deviation of the population.

d = (43 - 40) / 8 = 0.375

This means that the mean self-esteem score of the sample is 0.375 standard deviations higher than the population mean self-esteem score.

Therefore,  The mean self-esteem score after the program (M = 43) is not significantly different from the population mean self-esteem score (μ0 = 40) at the α = 0.05 level.

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The length of the wire with a radius of 0.236 millimeters is 16.5 cm.

We are given the formula for the radius of a platinum wire in terms of its length L and resistance R:

[tex]r = 0.059L^{(1/2) } \ mm[/tex]

We are also told that the resistance of the wire is 0.1 ohm.

We can use the formula for the resistance of a wire in terms of its length L, cross-sectional area A, and resistivity rho:

R = ρL/A

where;

We can rearrange this formula to solve for the cross-sectional area:

A = ρL/R

Substituting the given values, we have:

A = (10.6 x 10⁻⁸ ohm. m)(L m)/(0.1 ohm)

A = 1.06 x 10⁻⁶ m L

We can also use the formula for the area of a circle in terms of its radius:

A = πr²

Solving for the radius, we have:

r = √(A/π)

Substituting the expression for A, we have:

r = √[(1.06 x 10⁻⁶ m.L )/π]

Substituting the given radius of 0.236 mm, we can solve for the length L:

0.236 x 10⁻³ m = √[(1.06 x  10⁻⁶ m.L)/π]

Squaring both sides, we have:

(0.236 x 10⁻³ m)² = (1.06 x 10⁻⁶ m.L)/π

Solving for L, we have:

L = [(0.236 x 10⁻³ m)² π]/(1.06 x  10⁻⁶ m)

L = 0.165 m = 16.5 cm

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Answer:

15s + 225 is less than or equal to 521

Step-by-step explanation:

The restaurant needs 521 spoons and it only has 225.

There is a very simple answer for this.  

If each set on sale contains 15 spoons (algorithm rule)

So determine s (15 x s) = 15s (calculation principle)

then 15s + 225 is less than or equal to 521

therefore the result is 15s + 225 is less than or equal to 521 spoons

The student can use a two-sample t-test to determine if there is a significant difference between the mean number of errors made by brand A and brand B. The two-sample t-test compares the means of two populations to determine if they are significantly different from each other.

The null hypothesis for this test is that the mean number of errors for brand A is equal to the mean number of errors for brand B. The alternative hypothesis is that the mean number of errors for brand A is less than the mean number of errors for brand B.

To conduct the two-sample t-test, the student will need to calculate the mean and standard deviation of the number of errors for each brand. Then, he will use the t-test formula to calculate the t-value and compare it to the critical value for a 5% level of significance.

If the t-value is less than the critical value, the student can reject the null hypothesis and conclude that the mean number of errors for brand A is significantly less than the mean number of errors for brand B. This would suggest that brand A is better than brand B.

However, if the t-value is greater than the critical value, the student cannot reject the null hypothesis and cannot conclude that there is a significant difference between the two brands.

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Answer:

There are duplicate letter choices for example, two E's and three Hs so be sure to choose the right one

1, ⇔ A   3221.21

2 ⇔ E   10.13

3 ⇔ H  133.63

4 ⇔  L    11.59

---------------------------------------

5 ⇔  H   346.77

6  ⇔  E   1.35

7   ⇔  R   0.54

8.  ⇔ T    0.02

----------------------------------

9 ⇔  O  [tex]f(t) = 33,000( 1- 0.27)^t[/tex]

10 ⇔ H  [tex]f(t) = 9.56(1.03)^t[/tex]

11 ⇔  F   [tex]f(t) = 5(1+ 0.125)^t\\[/tex]

12 ⇔  T  [tex]f(t) = 4000(1.01)^t[/tex]

Step-by-step explanation:

These questions can be solved by plugging in the value of each of the given variables into each equation and solving using a calculator

I will provide the solution steps for one from each batch.
Q1 - Q4
t  = 4

Q1.
[tex]y =275 ( 1 + 0.85)^4\\\\= 275(1.85)^4\\\\= 275 \times 11.71350625\\\\= 3221. 21 \text{ to the nearest hundredth}[/tex]

You really don't have to compute (1.85)⁴ separately; most calculators can do everything in one shot

Correct answer: A

-----------------------------------------------------------------------------------------------------

5 - 8
Q8
[tex]h(t) = 0.8\left(\dfrac{3}{5}\right)^t \\\\\text{When t = 7}\\h(7) = 0.8\left(\dfrac{3}{5}\right)^7 \\\\= 0.8(0.6)^7 \;\;\;\;\left(\dfrac{3}{5} = 0.6} \right)\\\\= 08 \times 0.0279936\\\\= 0.02239488\\\\= 0.02\text{ to the nearest hundredth}[/tex]

Corresponds to T

--------------------------------------------------------------------------------------------

9 - 12

You can determine all of these by looking at the multiplier in the given equations for f(t) where the multiplier is the constant outside the parentheses

Question 9
Multiplier is 33,000 so the equation is
[tex]f(t) = 33,000( 1- 0.27)^t[/tex]   ==> O

Question 10
Answer choice ==> H

Question 11
Answer Choice ==> F

Question 12
Answer choice ==> T

The required area of the sector is  106 sq units.

A part of a circle's interior is called a segment. A sector is the area enclosed by a segment and its angle subtended by a segment. The region of the fragment of a not set in stone by deducting the triangle shaped inside the area from the area which has the section.

We have given

Radius of sector = 9 ft and angle of sector = 150°

[tex]$Area of sector = \frac{angle}{360}\times\pi r^2[/tex]

[tex]Area of sector = \frac{150}{360} \times\pi 9^2[/tex]

Area of sector = 106 sq units.

Thus, required area of the sector is  106 sq units.

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Answer:

23,520

Step-by-step explanation:

The population of an island has decreased by 2% when the population was 24000. What we want to do is find out how much of a population is each percentage. We want to divide 24,000 with 100 because 24,000 is 100% of the population 10 years ago.

24,000 ÷ 100 = 240

Now we know 1% of the population is 240, but we want to find out 2% of the population. Now we want to multiply by 2.

240 × 2 = 480

Now we know the population has decreased by 480 over the last 10 years, but we want to know the population of the island now. This is easy, all we got to do is take the original population and subtract how much the population it has decreased over 10 years.

24,000 - 480 = 23,520

The population of the island now is 23,520

Hope this helps : )

Answer:

23,520

Step-by-step explanation:

A percentage is a ratio or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

If the island had a population of 24,000 10 years ago, we could solve for the population decrease by using this expression:

Well, if percentages are fractions of 100, this means that 2% is equivalent to [tex]\frac{2}{100}[/tex], which is also equivalent to 0.02.

This means over the past 10 years the population decreased by 480.

Now that we know this, we can subtract that from the total amount to get the population now.

This means that the population of the island now is 23,520.

Therefore, the population of the island now with a 2% decrease is 23,520.

Answer:

[tex]\frac{2x^{4} - 5x^{2} + x + 6 }{x}[/tex]

Step-by-step explanation:

[tex]\frac{2x^{3} - 5x + \frac{6}{x} + 1 }{x}[/tex]
[tex]\frac{2x^{4} - 5x^{2} + x + 6 }{x}[/tex]

[tex]2 {x}^{2} - 2x - 3[/tex]

step by step explanations

Answer:

242 cm

Step-by-step explanation:

20x12x0.2=242

The statement that isn't true is:

B. The median can be different from all of the data values.

The median of a set of data is the middle value when the data is arranged in order from smallest to largest.  

Let's check the given options

A. The median can be the same value as the IQR.

This statement is true, as the IQR is defined as the difference between the third quartile (Q3) and the first quartile (Q1), which are both data values that can include the median.

C. The median can be less than the lower quartile.

This statement is true, as the median is simply the middle value of the dataset when it is arranged in order, whereas the lower quartile (Q1) is the value that separates the bottom 25% of the data from the top 75%.

D. The median can be the same value as the mean.

This statement is true in a symmetric distribution, where the mean and median are equal. However, in skewed distributions, the mean and median can be different values.

B. The median can be different from all of the data values.

The median is a value that divides the dataset into two equal halves. It is always a data value, and it is not possible for the median to be different from all of the data values.  

Therefore,

The statement that isn't true is:

B. The median can be different from all of the data values.

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a. The total cost is $310.64. b. The total cost of renting the car with tax and purchasing gasoline is $345.99.

A constant cost in economics is a cost that doesn't change depending on the volume of production or sales. Rent, wages, and insurance premiums are some instances of fixed costs. Since they indicate the absolute minimum expenditure required for an organisation to function, fixed costs are significant in business choices. Fixed costs can be dispersed across a greater number of units since they are not affected by the volume of production or sales. This can lower the per-unit cost of manufacturing.

Given that, the car rents for $229.00 per week with no charge for mileage. Her gasoline cost is $81.64.

a. Total cost = $229.00 + $81.64 = $310.64

b. If the rental is subject to a 15% state and local tax, then the additional cost is:

0.15 x $229.00 = $34.35

$229.00 + $34.35 + $81.64 = $345.99

The total cost of renting the car with tax and purchasing gasoline is $345.99.

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The cοrrect οptiοn is Optiοn D. The p-value is less than α, and the null hypοthesis is nοt rejected. There is nο cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.

Frοm the given data,

A cοmpany that ships glass fοr a manufacturer claimed that its shipping bοxes are cοnstructed sο that nο mοre than 8 percent οf the bοxes arrive with brοken glass.

The glass manufacturer believes that the actual percentage is greater than 8 percent.

The manufacturer tested the hypοtheses

H0: p = 0.08 and Ha: p > 0.08

The test yielded a p-value οf 0.1

Since the significance level (alpha) is 0.1 and the calculated p-value is 0.1,

we cοmpare the p-value tο alpha.

If the p-value is less than οr equal tο alpha, we reject the null hypοthesis H0: p = 0.08 in favοr οf the alternative hypοthesis Ha: p > 0.08.

If the p-value is greater than the alpha, we fail tο reject the null hypοthesis.

In this case, the calculated p-value οf 0.1 is greater than the significance level οf 0.1.

Therefοre, we fail tο reject the null hypοthesis and cοnclude that there is nοt enοugh evidence tο suppοrt the claim that the actual prοpοrtiοn οf bοxes with brοken glass is greater than 8%.

It is pοssible that the cοmpany's claim οf nο mοre than 8% brοken bοxes is accurate.

Therefοre,

The cοrrect οptiοn is Optiοn D.

The p-value is less than α, and the null hypοthesis is nοt rejected. There is nο cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.

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Cοmplete questiοn:

A cοmpany that ships glass fοr a glass manufacturer claimed that its shipping bοxes are cοnstructed sο that nο mοre than 8 percent οf the bοxes arrive with brοken glass. The glass manufacturer believed the actual percent is greater than 8 percent. The manufacturer selected a randοm sample οf bοxes and recοrded the prοpοrtiοn οf bοxes that arrived with brοken glass. The manufacturer tested the hypοtheses H0:p=0.08 versus Ha:p>0.08 at the significance level οf α=0.01.

The test yielded a p-value οf 0.001. Assuming all cοnditiοns fοr inference were met, which οf the fοllοwing is the cοrrect cοnclusiοn?

The p-value is less than α, and the null hypοthesis is nοt rejected. There is nοt cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.

The p-value is less than α, and the null hypοthesis is nοt rejected. There is nοt cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.

The p-value is greater than α, and the null hypοthesis is rejected. There is nοt cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08

The p-value is less than α, and the null hypοthesis is nοt rejected. There is nοt cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.

Answer:

The Interquartile Range or (IQR) is 24

Step-by-step explanation:

Since the data set is ordered, we don't need to order it.

Now, to find the interquartile range:

First, find median which is 65 since it is in the middle

Next, we find the median in Quartile 1 and Quartile 3 (Quartile 2 is median)

So in Quartile 1, median is 47

Quartile 2, median is 71

Now find the range of those two:

71 - 47 = 24

Hope this helps!!

Using the circumference, the area of the hub cap is obtained as approximately 437.21 square centimeters.

What is circumference?

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area.

The circumference of the hub cap is given by the formula -

C = 2πr

where r is the radius of the hub cap.

We can solve for the radius by dividing both sides by 2π -

r = C / 2π

r = 74.04 / 2(3.14)

r ≈ 11.8 cm

The area of the hub cap is given by the formula -

A = πr²

Substituting the value of r in the equation, we get  -

A = π(11.8)²

A = 3.14 × 139.24

A ≈ 437.21 cm²

Therefore, the area of the hub cap is 437.21 square centimeters.

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Answer:

We are given that the probability of landing on 2 is twice the probability of landing on 3, and the relative frequencies of landing on 1 and 4 are 0.1 and 0.3 respectively.

Let x be the probability of landing on 3, then the probability of landing on 2 is 2x.

The sum of probabilities of all possible outcomes is 1, so we can write:

0.1 + 2x + x + 0.3 = 1

Simplifying this equation, we get:

3x + 0.4 = 1

3x = 0.6

x = 0.2

Therefore, the probability of landing on 3 is 0.2 and the probability of landing on 2 is 2x = 0.4.

If the spinner is spun 50 times, we can expect it to land on 2 approximately 0.4 * 50 = 20 times

Step-by-step explanation:

If any doubt Ask Me

The length of QS in parallelogram RSTU is 7c - 1.

A parallelogram is a quadrilateral with two pairs of parallel sides. This means that opposite sides of the parallelogram are parallel and have the same length. Additionally, opposite angles of a parallelogram are congruent, meaning they have the same measure.

Some important properties of parallelograms include:

Diagonals bisect each other: The diagonals of a parallelogram bisect each other. This means that the point where the diagonals intersect is the midpoint of each diagonal.

Opposite sides are congruent: The opposite sides of a parallelogram are congruent. This means that they have the same length.

Consecutive angles are supplementary: Consecutive angles of a parallelogram are supplementary, meaning they add up to 180 degrees.

Each pair of opposite sides is parallel: In a parallelogram, each pair of opposite sides is parallel. This means that the distance between the parallel sides is constant along the length of the parallelogram.

In a parallelogram, opposite sides are equal in length. Therefore, if we can find the length of TU, we can use it to find the length of QS.

To find TU, we can use the fact that SU and RT are diagonals that intersect at Q. Since diagonals of a parallelogram bisect each other, we know that QU = QT and QS = QS. Therefore, we can write:

TU = QU + QS = (c + 7) + (6c - 8) = 7c - 1

Now that we know TU, we can use it to find QS. Since QS = TU, we have:

QS = 7c - 1

Therefore, the length of QS in parallelogram RSTU is 7c - 1.

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Answer: 5 percent

Step-by-step explanation:

Step-by-step explanation:

1year=12month

8years =12×8=86month

11/100×12000=1320

12000-1320=10680

10680/86

they will deposit 124

In the quadrilateral the measure of angles in ratio 7 : 9 is 70° and 90°. respectively.

What is an angle?

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

The sum of the angles of a quadrilateral is always 360 degrees.

So, we can start by finding the measure of the two unknown angles using the information that we have -

Let x be the measure of the smaller of the two unknown angles, then the measure of the larger angle is 9x and smaller angle is 7x (since the two angles are in a ratio of 7:9).

The sum of all four angles is 140° + 60° + 7x + 9x = 360°.

Simplifying this equation, we get -

140° + 60° + 16x = 360°

200° + 16x = 360°

16x = 160°

Dividing both sides by 16, we get -

x = 10°

So, the smaller of the two unknown angles is -

7x = 7 × 10° = 70°

The larger angle is -

9x = 9 × 10° = 90°

Therefore, the measures of the two unknown angles are 70° and 90°.

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Using the corresponding and alternate angles, we found the measures of the following angles:

1) m∠ABE = 82°

2) m∠EBF = 53°

3) m∠BFE = 45°

4) m∠BEF = 82°

What are corresponding angles?

Corresponding angles are those that are created when two parallel lines are intersected by another line, whether it be a transversal or a matching corner (i.e. the transversal). According to the definition of corresponding angles, when two parallel lines are intersected by a third line, the angles that are present at each intersection and are in the same relative position are said to be corresponding angles.

The angles created when a transversal cuts two straight lines are known as alternative angles, and they are formed on the opposite side of the transversal with regard to both lines.

Here the lines AC and DF are parallel to each other.

The line EB cuts them.

So corresponding angles are formed.

∠DEB = ∠ABG = 98°

Now ∠ABG + ∠ABE = 180°

So ∠ABE = 180 - ∠ABG = 180 - 98 = 82°

∠ABE + ∠EBF + 45° = 180°

82 + ∠EBF + 45 = 180

∠EBF = 53°

∠BFE = ∠FBE = alternate angles

∠BFE = 45°

∠BEF = ∠ABE = alternate angles

∠BEF = 82°

Therefore using the corresponding and alternate angles, we found the measures of the following angles:

1) m∠ABE = 82°

2) m∠EBF = 53°

3) m∠BFE = 45°

4) m∠BEF = 82°

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