Using the Incenter P, find the measure of ∠ZPX.




117°

140°

64°

129°

42°

132°

Using The Incenter P, Find The Measure Of ZPX.1171406412942132

Answers

Answer 1

Answer:

The measure of ∠ZPX is 63°

Step-by-step explanation:

The given parameters are;

The incenter of the triangle = P

m∠KXP = 31°, m∠PYJ = 27°, [tex]\overline {ZP}[/tex] = 20 feet

Given that the segment [tex]\overline {XJ}[/tex] from the vertex, X, passes through the incenter of the triangle, we have;

The segment [tex]\overline {XJ}[/tex] bisects ∠KXL to form ∠KXP and ∠LXP

Therefore, ∠KXP = ∠LXP = 31°

∠KXL = ∠KXP + ∠LXP = 31° + 31° = 62°

∠KXL = 62°

Similarly;

The segment [tex]\overline {YL}[/tex] bisects ∠KYJ to form ∠PYJ and ∠PYK

Therefore, ∠PYJ = ∠PYK = 27°

∠KYJ = ∠PYJ  + ∠PYK = 27° + 27° = 54°

∠KYJ = 54°

In ΔXYZ, we have, ∠LZJ + ∠KYJ + ∠KXL = 180° based on the sum of the interior angles of a triangle postulate

∴ ∠LZJ = 180° - (∠KYJ + ∠KXL) = 180° - (54° + 62°) = 64°

∠LZJ = 64°

The segment [tex]\overline {ZK}[/tex] bisects ∠LZJ to form ∠PZL and ∠PZJ

Therefore, ∠PZL = ∠PZJ

∠LZJ = ∠PZL + ∠PZJ = 2 × ∠PZL = 64°

∠PZL = 64°/2 = 32° = ∠PZJ

In ΔZPX, we have;

∠PZL + ∠LXP + ∠ZPX = 180° based on the sum of the interior angles of a triangle postulate

∠ZPX = 180° - (∠PZL + ∠LXP) = 180° - (32° + 31°) = 63°

∠ZPX = 63°

The measure of ∠ZPX = 63°


Related Questions

The tables below represent different ratios of teaspoons of sugar to ounces of iced tea. Which table represents the greatest ratio of sugar-to-iced tea?

Answers

Answer:

Option (C)

Step-by-step explanation:

Option A.

Ratio of table spoons of sugar to ounces of iced tea = [tex]\frac{\text{Amount of sugar (in oz)}}{\text{Amount of ice tea (in oz)}}[/tex]

From the table attached,

Ratio = [tex]\frac{6}{24}[/tex]

         = 1 : 4

Option B.

Ratio of sugar to ounces of iced tea = [tex]\frac{3}{18}[/tex]

                                                            = 1 : 6

Option C.

Ratio of sugar to ounces of iced tea = [tex]\frac{1}{3}[/tex]

                                                            = 1 : 3

Option D.

Ratio of sugar to ounces of iced tea = [tex]\frac{7}{24}[/tex]

                                                            = 7 : 24

                                                            ≈ 1 : 3.43

Since, highest ratio means biggest fraction (with least denominator).

From the given options, biggest fraction is [tex]\frac{1}{3}[/tex].

Therefore, highest ratio of amount of sugar in (tsp) to number of ounces of ice tea is in Option (C).

entlying
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Answers

Answer:

B... Because indicates the direction of gravity because its direction is downward

Answer:b

Step-by-step explanation:

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Answers

Answer:

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Hope this helps and if you could mark this as brainliest. Thanks!

Answer:

-0.2x

Step-by-step explanation:

If x is negative then,

-0.2(-2) = 0.4

Identify the variable(s), set up your equation(s), and solve. Richard has an elder sister who is twice his age and a younger sister who is two years younger than him. If the product of his sisters' ages is 70, how old is Richard?

Answers

Answer:

7 years

Step-by-step explanation:

Given that:

Let Richard's age = x

Elder sister's age = 2x

Youngwr sister's age = x - 2

Product of sisters ages = 70

2x * (x - 2) = 70

2x² - 4x = 70

2x² - 4x - 70 = 0

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x² - 7x + 5x - 35 = 0

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Answers

Answer:

x = -1/7

Step-by-step explanation:

25x - 15x = x - 1

combine like terms

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divide

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Answer:

x = -1/7 (the whole fraction is negative)

Step-by-step explanation:

23x−15x=x−1

8x = x - 1

8x - x = x - 1 - x

7x = -1

x = -1/7

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Answers

Answer:

If u mean plymouth rock then the answer is

Lost at sea, they happened upon a piece of land that would become known as Cape Cod. After surveying the land, they set up camp not too far from Plymouth Rock. ... The 102 travellers aboard the Mayflower landed upon the shores of Plymouth in 1620. This rock still sits on those shores to commemorate the historic event.

Step-by-step explanation:

12x² + 8x = 0
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Answers

Answer:

The zeros are at 0 and -2/3

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Answers

Answer:

-3 = -v + 7

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Step-by-step explanation:

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i hope this helps....

have a great day ahead :)

Answer:

v = 10

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answers

Answer:

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Step-by-step explanation:

The point slope form is;

y-y1 = m(x-x1)

where m represents the slope

(x1, y1) represents the given point

Thus;

y-5 = -4(x + 2)

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

Angle of depression = 3.37°

Step-by-step explanation:

We are told that A plane flies at an altitude of 3.5 kilometers and then starts to descend when it is 60

kilometers from the runway.

I've attached an image of a triangle depicting this question.

From the triangle, we can find the angle of depression θ from trigonometric ratio since it's a right angle triangle.

Thus;

3.5/60 = tan θ

tan θ = 0.0583

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answer:

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Step-by-step explanation:

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Answers

Answer:

f(x) = [tex]\frac{1}{2}[/tex] [tex](2)^{x}[/tex]

Step-by-step explanation:

Using the standard form of the exponential function

y = a [tex]b^{x}[/tex]

To find a and b , substitute ordered pairs from the graph

Using (0, 0.5 ), then

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a = 0.5 , so

y = [tex]\frac{1}{2}[/tex] [tex]b^{x}[/tex]

Using (1, 1) , then

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Answers

Answer:

B. 6 miles

Step-by-step explanation:

first you convert the hour and 12 minutes into only minutes

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Answers

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Answers

Answer: n greater than or equal to 96 or n is greater than or less than 318

Step-by-step explanation:

Brainliest plz

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2. 150 degrees
3. 225 degrees
4. 252 degrees

Answers

Answer:

252°

Step-by-step explanation:

Given

Shape: Decagon

Required

Determine the value of n

A Decagon has 10 sides and a complete rotation takes 360°

First, we need to calculate the angle of each rotation as follows.

Each Rotation = ⅒ * 360°

Each Rotation = 360°

Next, we determine the possible values of n.

The statement is represented as "possible values of n" because n can assume infinite number of values.

However, n must be a multiple of 36

From the list of given options.

10, 150 and 225 are not multiples of 36

Only 252 happens to be a multiple of 36 from the list of given options.

Hence, option D answers the question [base on the given options]

A decagon is a ten-sided polygon.

The value of n could be 252 degree.

Since, A Decagon has 10 sides

The angle made in one complete rotation is 360 degree.

Now find angle made in each rotation is,

                          [tex]=\frac{360}{10}=36degree[/tex]

Now, we have to find possible values of n.

Since, n must be a multiple of 36

Apply hit and trial from given option.

We observe that from given options, only 252 degree is multiple of 36.

Therefore, value of n could be 252 degree.

Hence, option 4  is correct.

Learn more:

https://brainly.com/question/9549251

You are tasked with buying pizza for a party that has 100 guests. 40 guests are children, and 60 guests are adults. Half of the children want pizza, and two thirds of the adults want pizza. Children will eat one slice of pizza, and adults will eat two slices of pizza. A pizza pie can be cut into 8 slices and costs $9 dollars per pie.

Answers

Total slices required for children,

[tex]C = \dfrac{40}{2}\times 1\\\\C = 20\ slices[/tex] .

Total slices required for adults,

[tex]A=\dfrac{2}{3}\times 60\times 2\\\\A = 80\ slices[/tex]

So, total slices required are, 20 + 80 = 100 .

Number of pizza, n = 100/8 = 12.5

So, he has to order 13 pizza cause pizza cannot be purchased in fraction.

Total price, P = 13 × 9 = $117 .

Hence, this is the required solution.

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Answers

Answer:

the pattern is +2, +6, +10, +14, +18 etc

so its in increment of 4

the rest is trivial

Step-by-step explanation:

Answer:

[tex]u_{n} = 2n^{2} -4n-3[/tex]

Step-by-step explanation:

a +b + c = - 5    First term in sequence

3a + b = 2   Difference between first two terms

2a = 4         Difference between  the difference of the first two terms and the second third terms (the difference between -5 and -3 is 2 the difference between -3 and 3 is 6; the difference between 6 and two is 4)

2a = 4 so a = 2; 3(2) + b = 2 → 6 + b = 2 so  b = -4; 2 - 4 + c = -5  → -2 + c = -5 so c = -3

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Answers

Answer:

5280

Step-by-step explanation:

I'm American and our system sucks but 1 mile is equal to 5280 feet

May I have brainliest please? :)

Answer:

I'm American and our system sucks but 1 mile is equal to 5280 feet

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Answers

Answer:

SSS

Step-by-step explanation:

I can identify that these triangles are congruent by using the SSS (Side, Side, Side) postulate theorem. I know this because first, second, and home triangle share the same side as the third, second, and home triangle, meaning they are congruent, so are the other sides of the angle since the question states they are congruent.

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Answers

Answer:

the decimals should line up.

Answer:

press the right arrow 3 times

Step-by-step explanation:

to properly subtract any numbers the value of the digits need to be in line

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Answers

Answer:

3a^2b-5ab^2

Step-by-step explanation:

Answer:

3a²b-5ab²

Step-by-step explanation:

Distribution method:

ab (3a-5b) = 3a²b-5ab²

y = (x - 4)(x-8)
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Answers

Answer:

[tex]y= x^{2} -12x+32[/tex]

Explanation:

[tex]y=x^{2} -8x-4x+32\\y= x^{2} -12x+32[/tex]

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