Question

If L is parallel to M, find the value of each missing variable(s)

Answer 1

Answer:

5. x = 13

6. x = 11; y = 3

Step-by-step explanation:

5. (9x + 2)° = 119° (alternate interior angles are congruent)

$9x + 2 = 119$

Subtract 2 from each side

$9x + 2 - 2 = 119 - 2$

$9x = 117$

Divide both sides by 9

$\frac{9x}{9} = \frac{117}{9}$

$x = 13$

6. (9x + 25)° = (13x - 19)° (corresponding angles are congruent)

$9x + 25 = 13x - 19$

Collect like terms

$9x - 13x = - 25 - 19$

$-4x = -44$

Divide both sides by -4

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

$x = 11$

(13x - 19)° + (17y + 5)° = 180° (linear pair)

$13x - 19 + 17y + 5 = 180$

Plug in the value of x and solve for y

$13(11) - 19 + 17y + 5 = 180$

$143 - 19 + 17y + 5 = 180$

Collect like terms

$129 + 17y = 180$

Subtract 129 from both sides

$129 + 17y - 129 = 180 - 129$

$17y = 51$

Divide both sides by 17

$\frac{17y}{17} = \frac{51}{17}$

$y = 3$