Answer:
m∠8 = 39°
Step-by-step explanation:
Given:
m∠3 = (4x−7)°
m∠5 = (6x−81)°
Required:
m∠8?
Solution:
First, find the value of x.
Since, line m is parallel to line n, therefore,
m∠3 = m∠5 (alternate interior angles are congruent)
[tex] 4x - 7 = 6x - 81 [/tex] (substitution)
Collect like terms
[tex] 4x - 6x = 7 - 81 [/tex]
[tex] -2x = -74 [/tex]
Divide both sides by -2
[tex] x = \frac{-74}{-2} [/tex]
[tex] x = 37 [/tex]
Find m∠8:
m∠8 + m∠5 = 180° (linear pair)
m∠8 + (6x - 81)° = 180° (substitution)
Plug in the value of x
m∠8 + (6(37) - 81)° = 180°
m∠8 + (222 - 81)° = 180°
m∠8 + 141° = 180°
Subtract 141 from both sides
m∠8 = 180° - 141°
m∠8 = 39°
