Mathematics, 20.09.2020 04:01 yehnerthannah

Can anyone please do these questions? This is Unit 1 Geometry basics Homework 5 Angle Relationships.

Can anyone please do these questions? This is Unit 1 Geometry basics Homework 5 Angle Relationships

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Answer from: nmulder

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. 6x + 7 $ and $ 8x - 17 are vertical angles.

Since vertical angles are congruent, therefore:

6x + 7 = 8x - 17

Solve for x

$6x - 8x = -7 - 17\\\\-2x = -24\\\\x = 12$

12. 11x - 15 $ and $ 5x - 13 are linear pair angles.

Since, the sum of linear pair angles equals 180 degrees, therefore:

(11x - 15) + (5x - 13) = 180

Solve for x

$11x - 15 + 5x - 13 = 180\\\\16x - 28 = 180\\\\16x - 28 + 28 = 180 + 28\\\\16x = 208\\\\x = 13$

13. <DBE and <CBE are complementary angles.

Since the some of complementary angles equals 90 degrees, therefore,

$m \angle DBE + m \angle CBE = 90$

Substitute

(2x - 1) + (5x - 42) = 90

Solve for x

$2x - 1 + 5x - 42 = 90\\\\7x - 43 = 90\\\\7x = 90 + 43\\\\7x = 133\\\\x = 19$

14. Since QS bisects <PQR, therefore,

m<PQS = 1/2(PQR)

Substitute

$10x + 1 = \frac{1}{2} (82)$

Solve for x

$10x + 1 = 41\\\\10x = 41 - 1\\\\10x = 40\\\\x = 4$

15. (x + 10) $ and $ (10x - 16) are linear pair angles.

Since the sum of linear pair angles equals 180 degrees, therefore,

$(x + 10) + (10x - 16) = 180\\$

Solve for x

$x + 10 + 10x - 61 = 180\\\\11x - 51 = 180\\\\11x = 180 + 51\\\\11x = 231\\\\x = 21$

Find y:

Since (10x - 61) $ and $ (10y + 5) are vertical angles, they are congruent. Therefore,

(10x - 61) = (10y + 5)

Plug in the value of x and solve for y

$10(21) - 61 = 18y + 5\\\\149 = 18y + 5\\\\149 - 5 = 10y\\\\144 = 18y\\\\8 = y\\\\\mathbf{y = 8}$

16. Since (5x - 17) $ and $ (3x - 11) are linear pair, their sum equals 180 degrees. Therefore,

(5x - 17) + (3x - 11) = 180

Solve for x

$5x - 17 + 3x - 11 = 180\\\\8x - 28 = 180\\\\8x = 180 + 28\\\\8x = 208\\\\x = 26$

Find y:

(2y + 5) + 90 + (3x - 11) = 180 (angles on a straight line = 180 degrees)

Plug in the value of x and solve for y

$2y + 5 + 90 + 3(26) - 11 = 180\\\\2y + 5 + 90 + 78 - 11 = 180\\\\2y + 162 = 180\\\\2y = 180 - 162\\\\2y =18\\\\y = 9$

17. Since NP bisects <MNQ, therefore,

$m \angle PNQ = \frac{1}{2}(m \angle MNQ)$

Substitute

$78 = \frac{1}{2}(8x + 12)$

Solve for x

$78 \times 2 = 8x + 12\\\\156 = 8x + 12\\\\156 - 12 = 8x \\\\144 = 8x\\\\18 = x\\\\x = 18$

$m \angle RNM + m \angle MNQ = 180^{\circ}$ (linear pair)

Substitute

(3y - 9) + (8x + 12) = 180

Plug in the value of x and solve for y

$3y - 9 + 8(18) + 12 = 180\\\\3y - 9 + 144 + 12 = 180\\\\3y + 147 = 180\\\\3y = 180 - 147\\\\3y = 33\\\\y = 11$

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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Answer from: jfrjtwrg

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 = $\frac{82}{2}$

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

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answer: h

step-by-step explanation:

Answer from: Quest

It will might be false

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