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find the measure of angle 8

Find The Measure Of Angle 8 class=

Sagot :

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

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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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