Answer:
[tex]\displaystyle 114° = m\angle{8}[/tex]
Step-by-step explanation:
Alternate Interiour Angles are congruent, so set both expressions equivalent to each other:
[tex]\displaystyle [-5x - 4]° = [-9x - 60]° \hookrightarrow \frac{56}{-4} = \frac{-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}[/tex]
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 [tex]\displaystyle 6\:and\:8[/tex]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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