Mathematics, 08.10.2020 06:01 emj617

Unit 3 parallel and perpendicular lines Homework 2, please help quickly

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Angles can be congruent based n several theorems; some of these theorems are: corresponding angles, vertical angles, alternate exterior angles and several others.

The values of x and y are:

5. $\mathbf{x = 13}$ 6. $\mathbf{x = 7}$ 7. $\mathbf{x= 26}$ 8. $\mathbf{x = 18}$ 9. $\mathbf{x = 11}$ and $\mathbf{y = 7}$ 10. $\mathbf{x = 24}$ and $\mathbf{y = 15}$ 11. $\mathbf{x = 18}$ and $\mathbf{y =5}$ 12. $\mathbf{x = 17}$ and $\mathbf{y=9}$

Question 5:

Angles (9x + 2) and 119 are alternate angles.

Alternate angles are equal. So, we have:

$\mathbf{9x +2 = 119}$

Subtract 2 from both sides

$\mathbf{9x = 117}$

Divide both sides by 9

$\mathbf{x = 13}$

Question 6:

Angles (12x - 8) and 104 are interior angles.

Interior angles add up to 180. So, we have:

$\mathbf{12x -8 + 104 = 180}$

Collect like terms

$\mathbf{12x = 180 - 104 + 8}$

$\mathbf{12x = 84}$

Divide both sides by 12

$\mathbf{x = 7}$

Question 7:

Angles (5x + 7) and (8x - 71) are alternate exterior angles.

Alternate exterior angles are equal. So, we have:

$\mathbf{5x + 7 = 8x - 71}$

Collect like terms

$\mathbf{8x - 5x= 71 + 7}$

$\mathbf{3x= 78}$

Divide both sides by 3

$\mathbf{x= 26}$

Question 8:

Angles (4x - 7) and (7x - 61) are corresponding angles.

Corresponding angles are equal. So, we have:

$\mathbf{4x - 7 = 7x - 61}$

Collect like terms

$\mathbf{4x - 7x = 7 - 61}$

$\mathbf{- 3x = -54}$

Divide both sides by -3

$\mathbf{x = 18}$

Question 9:

Angles (9x + 25) and (13x - 19) are corresponding angles.

Corresponding angles are equal. So, we have:

$\mathbf{9x + 25 = 13x - 19}$

Collect like terms

$\mathbf{9x -13x = -25 - 19}$

$\mathbf{-4x = -44}$

Divide both sides by -4

$\mathbf{x = 11}$

Angles (17y + 5) and (13x - 19) are supplementary angles.

So, we have:

$\mathbf{17y + 5 = 13x - 19}$

Substitute 11 for x

$\mathbf{17y + 5 = 13\times 11 - 19}$

$\mathbf{17y + 5 = 124}$

Subtract 5 from both sides

$\mathbf{17y = 119}$

Divide both sides by 17

$\mathbf{y = 7}$

Question 10:

Angles (3x - 29) and (6x - 7) add up to 180

So, we have:

$\mathbf{3x -29 + 6x - 7 = 180}$

Collect like terms

$\mathbf{3x + 6x = 180 + 7 + 29}$

$\mathbf{9x = 216}$

Divide both sides by 9

$\mathbf{x = 24}$

Angles (3x - 29) and (8y + 17) are supplementary angles.

So, we have:

$\mathbf{3x - 29 + 8y + 17 = 180}$

Substitute 24 for x

$\mathbf{3 \times 24 - 29 + 8y + 17 = 180}$

$\mathbf{43 + 8y + 17 = 180}$

Collect like terms

$\mathbf{8y = 180 - 43 - 17}$

$\mathbf{8y = 120}$

Divide both sides by 8

$\mathbf{y = 15}$

Question 11:

Angles (7x - 23) and (49 + 3x) are corresponding angles

So, we have:

$\mathbf{7x - 23 = 49 + 3x}$

Collect like terms

$\mathbf{7x - 3x = 49 + 23}$

$\mathbf{4x = 72}$

Divide both sides by 4

$\mathbf{x = 18}$

Angles 3x and (11y - 1) are corresponding angles.

So, we have:

$\mathbf{3x = 11y - 1}$

Substitute 18 for x

$\mathbf{3 \times 18 = 11y - 1}$

$\mathbf{54 = 11y - 1}$

Collect like terms

$\mathbf{11y =54+ 1}$

$\mathbf{11y =55}$

Divide both sides by 11

$\mathbf{y =5}$

Question 12:

Angles (5x - 38) and (3x - 4) are corresponding angles

So, we have:

$\mathbf{5x - 38 = 3x - 4}$

Collect like terms

$\mathbf{5x - 3x = 38 - 4}$

$\mathbf{2x = 34}$

Divide both sides by 2

$\mathbf{x = 17}$

Angles (7y - 20) and (5x - 38) are angles at the other legs of a right-angled triangle.

So, we have:

$\mathbf{7y - 20 +5x - 38 = 90}$

Substitute 17 for x

$\mathbf{7y - 20 +5 \times 17 - 38 = 90}$

$\mathbf{7y+ 27 = 90}$

Collect like terms

$\mathbf{7y=- 27 +90}$

$\mathbf{7y=63}$

Divide both sides by 7

$\mathbf{y=9}$

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Unit 3 parallel and perpendicular lines Homework 2, please help quickly
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