Question

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

Answer 1

5. x = 13

6. x = 11; y = 3

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

`(9x)/(9) = (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

`(-4x)/(-4) = (-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

`(17y)/(17) = (51)/(17)`

`y = 3`