Can anyone please do these questions? This is Unit 1 Geometry basics Homework 5 Angle Relationships.
Answers
Answer:
Step-by-step explanation:
11). 6x + 7 = 8x - 17 [Since vertical angles are equal in measure]
8x - 6x = 17 + 7
2x = 24
x = 12
12). (11x - 15) + (5x - 13) = 180°
16x - 28 = 180°
16x = 180 + 28
16x = 208
x = 13
13). Since DB⊥AC,
m∠CBD = 90°
m∠CBE + m∠DBE = 90°
(5x - 42) + (2x - 1) = 90°
7x - 43 = 90
7x = 133
x = 19
14). Since QS bisects angle PQR,
m∠PQS = m∠RQS
10x + 1 = [tex]\frac{82}{2}[/tex]
10x + 1 = 41
10x = 40
x = 4
15). 10x - 61 = 18y + 5 [Vertical angles]
10x - 18y = 61 + 5
10x - 18y = 66
5x - 9y = 33 ------(1)
(18y + 5) + (x + 10) = 180 [linear pair of angles are supplementary]
18y + x + 15 = 180
x + 18y = 165 ------(2)
By adding equation (1)×2 and equation (2)
(10x - 18y) + (x + 18y) = 66 + 165
11x = 231
x = 21
16). (5x - 17) + (3x - 11) = 180 [[linear pair of angles are supplementary]
8x - 28 = 180
8x = 180 + 28
8x = 208
x = 26
(3x - 11)° = 78 - 11
= 67°
67° + 90° + (2y + 5)°= 180° [Sum of angles on a line]
162 + 2y = 180
2y = 180 - 162
2y = 18
y = 9
17). NP bisects ∠MNQ.
Therefore, m∠MNQ = 2(m∠PNQ)
8x + 12 = 2×78
8x + 12 = 156
8x = 156 - 12
8x = 144
x = 18
m∠MNQ = (8x + 12)° = 156°
m∠RNM = m∠ONQ [Vertical angles]
(3y - 9)° = 180° - m∠MNQ
3y - 9 = 180 - 156
3y - 9 = 24
3y = 33
y = 11
Using the knowledge of the angle relationships to create an equation, the value of x and y in the image given are:
11. x = 12
12. x = 13
13. x = 19
14. x = 4
15. x = 21; y = 8
16. x = 26; y = 9
17. x = 18; y = 11
Applying the knowledge of angle relationships, we can solve each given problem by first, creating a an equation from the relationship between angles, then solve for the variables.
11. [tex]6x + 7 $ and $ 8x - 17[/tex] are vertical angles.
Since vertical angles are congruent, therefore:[tex]6x + 7 = 8x - 17[/tex]
Solve for x[tex]6x - 8x = -7 - 17\\\\-2x = -24\\\\x = 12[/tex]
12. [tex]11x - 15 $ and $ 5x - 13[/tex] are linear pair angles.
Since, the sum of linear pair angles equals 180 degrees, therefore:[tex](11x - 15) + (5x - 13) = 180[/tex]
Solve for x[tex]11x - 15 + 5x - 13 = 180\\\\16x - 28 = 180\\\\16x - 28 + 28 = 180 + 28\\\\16x = 208\\\\x = 13[/tex]
13. <DBE and <CBE are complementary angles.
Since the some of complementary angles equals 90 degrees, therefore,[tex]m \angle DBE + m \angle CBE = 90[/tex]
Substitute[tex](2x - 1) + (5x - 42) = 90[/tex]
Solve for x[tex]2x - 1 + 5x - 42 = 90\\\\7x - 43 = 90\\\\7x = 90 + 43\\\\7x = 133\\\\x = 19[/tex]
14. Since QS bisects <PQR, therefore,
m<PQS = 1/2(PQR)
Substitute[tex]10x + 1 = \frac{1}{2} (82)[/tex]
Solve for x[tex]10x + 1 = 41\\\\10x = 41 - 1\\\\10x = 40\\\\x = 4[/tex]
15. [tex](x + 10) $ and $ (10x - 16)[/tex] are linear pair angles.
Since the sum of linear pair angles equals 180 degrees, therefore,[tex](x + 10) + (10x - 16) = 180\\[/tex]
Solve for x[tex]x + 10 + 10x - 61 = 180\\\\11x - 51 = 180\\\\11x = 180 + 51\\\\11x = 231\\\\x = 21[/tex]
Find y:Since [tex](10x - 61) $ and $ (10y + 5)[/tex] are vertical angles, they are congruent. Therefore,
[tex](10x - 61) = (10y + 5)[/tex]
Plug in the value of x and solve for y[tex]10(21) - 61 = 18y + 5\\\\149 = 18y + 5\\\\149 - 5 = 10y\\\\144 = 18y\\\\8 = y\\\\\mathbf{y = 8}[/tex]
16. Since [tex](5x - 17) $ and $ (3x - 11)[/tex] are linear pair, their sum equals 180 degrees. Therefore,
[tex](5x - 17) + (3x - 11) = 180[/tex]
Solve for x[tex]5x - 17 + 3x - 11 = 180\\\\8x - 28 = 180\\\\8x = 180 + 28\\\\8x = 208\\\\x = 26[/tex]
Find y:[tex](2y + 5) + 90 + (3x - 11) = 180[/tex] (angles on a straight line = 180 degrees)
Plug in the value of x and solve for y[tex]2y + 5 + 90 + 3(26) - 11 = 180\\\\2y + 5 + 90 + 78 - 11 = 180\\\\2y + 162 = 180\\\\2y = 180 - 162\\\\2y =18\\\\y = 9[/tex]
17. Since NP bisects <MNQ, therefore,
[tex]m \angle PNQ = \frac{1}{2}(m \angle MNQ)[/tex]
Substitute[tex]78 = \frac{1}{2}(8x + 12)[/tex]
Solve for x[tex]78 \times 2 = 8x + 12\\\\156 = 8x + 12\\\\156 - 12 = 8x \\\\144 = 8x\\\\18 = x\\\\x = 18[/tex]
[tex]m \angle RNM + m \angle MNQ = 180^{\circ}[/tex] (linear pair)
Substitute[tex](3y - 9) + (8x + 12) = 180[/tex]
Plug in the value of x and solve for y[tex]3y - 9 + 8(18) + 12 = 180\\\\3y - 9 + 144 + 12 = 180\\\\3y + 147 = 180\\\\3y = 180 - 147\\\\3y = 33\\\\y = 11[/tex]
Therefore, using the knowledge of the angle relationships to create an equation, the value of x and y in the image given are:
11. x = 12
12. x = 13
13. x = 19
14. x = 4
15. x = 21; y = 8
16. x = 26; y = 9
17. x = 18; y = 11
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer and Step-by-step explanation:
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Hope this helped you out! Have a wonderful day!
**Note, I didn't understand what you were asking, that's why I went into so much detail to help you out. Please, be clearer with your questions. Make sure you got all the whole question in there! Thank you!**
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
Statement Reason
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Step-by-step explanation:
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Step-by-step explanation:
PLZ MARK BRAINLIEST
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Answer:
a=18
Step-by-step explanation:
The value of a or m is 18 in the linear equation, y = 5x - 2.
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Given:
The table represents a linear function.
The data is given in the attached image.
The general equation of the linear function is,
y = ax+b.
Where a is the slope and b is constant.
By using the first and the third points from the table to find the equation of the linear function,
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13 = 3a+b {equation 1}
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we get,
a = 5 and b = -2
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y = 5x - 2
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Answer:
Step-by-step explanation:
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The cost of one pound beef is $3.2
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As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Cost 4.5 pound of beef = $14.40
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Can I get all the right answers only
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Answer:
yes, you can get all right answers.
Answer:
yes i believe that you can get all the answers right
Step-by-step explanation:
what is 660 increased by 1 followed by a further one
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660+1+1= 662
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Answer:
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2(4x - 3)=3(x+8)
The equation above is the problem I’m stuck on, I’m in algebra two and it’s been awhile since we’ve gone over this type of equation.
Answers
Answer:
x = 6
Step-by-step explanation:
2(4x - 3) = 3(x + 8)
1. Distribute the 2 and 3 into the parentheses.
2(4x) + 2(-3) = 3(x) + 3(8)
= 8x - 6 = 3x + 24
2. Subtract 3x from both sides.
8x - 3x - 6 = 3x - 3x + 24
= 5x - 6 = 24
3. Add 6 on both sides.
5x - 6 + 6 = 24 + 6
5x = 30
4. Divide by 5.
5x ÷ 5 = 30 ÷ 5
x = 6
Hope that helps.