Answer:
5. x = 13
6. x = 11; y = 3
Step-by-step explanation:
5. (9x + 2)° = 119° (alternate interior angles are congruent)
[tex] 9x + 2 = 119 [/tex]
Subtract 2 from each side
[tex] 9x + 2 - 2 = 119 - 2 [/tex]
[tex] 9x = 117 [/tex]
Divide both sides by 9
[tex] \frac{9x}{9} = \frac{117}{9} [/tex]
[tex] x = 13 [/tex]
6. (9x + 25)° = (13x - 19)° (corresponding angles are congruent)
[tex] 9x + 25 = 13x - 19 [/tex]
Collect like terms
[tex] 9x - 13x = - 25 - 19 [/tex]
[tex] -4x = -44 [/tex]
Divide both sides by -4
[tex] \frac{-4x}{-4} = \frac{-44}{-4} [/tex]
[tex] x = 11 [/tex]
(13x - 19)° + (17y + 5)° = 180° (linear pair)
[tex] 13x - 19 + 17y + 5 = 180 [/tex]
Plug in the value of x and solve for y
[tex] 13(11) - 19 + 17y + 5 = 180 [/tex]
[tex] 143 - 19 + 17y + 5 = 180 [/tex]
Collect like terms
[tex] 129 + 17y = 180 [/tex]
Subtract 129 from both sides
[tex] 129 + 17y - 129 = 180 - 129 [/tex]
[tex] 17y = 51 [/tex]
Divide both sides by 17
[tex] \frac{17y}{17} = \frac{51}{17} [/tex]
[tex] y = 3 [/tex]
