Question

Find the measure of angle 8

Answer 1

Angle 8 = 114
Since the two lines are parallel, -9x -60 is corresponding to angle two. Angle two is vertical and therefore equal to -5x -4,
-9x-60=-5x-4
-4x=56
X= -14
-9x-60 + angle 8 = 180 (supplementary angles)
126-60 + angle 8 = 180
Angle 8 = 180-66
Angle 8= 114

Answer 2

`\displaystyle 114° = m\angle{8}`

Explanation:

Alternate Interiour Angles are congruent, so set both expressions equivalent to each other:

`\displaystyle [-5x - 4]° = [-9x - 60]° \hookrightarrow (56)/(-4) = (-4x)/(-4) \\ \\ -14 = x \\ \\ \\ 180° = [-9(-14) - 60]° + m\angle{8} \hookrightarrow 180° = [126 - 60]° + m\angle{8}; 180° = 66° + m\angle{8} \\ \\ 114° = m\angle{4}`

As you can see, we plugged the x-value into the expression for the sixth angle because if you recall, you can tell that angles
`\displaystyle 6\:and\:8`form a linear pair, and accourding to the Linear Pair Theorem, these angles are considered supplementary, therefore one hundred fourteen degrees is the measure of the eight angle.

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