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find the measure of angle 1

Find The Measure Of Angle 1 class=

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Answer:

[tex]\displaystyle 70° = m\angle{1}[/tex]

Step-by-step explanation:

Consecutive Interiour Angles are supplementary, so set both expressions equivalent to one hundred eighty degrees:

[tex]\displaystyle 180° = [9x + 38]° + [6x + 22]° \hookrightarrow 180° = [60 + 15x]° \hookrightarrow \frac{120}{15} = \frac{15x}{15} \\ \\ 8 = x \\ \\ \\ [6[8] + 22]°; [48 + 22]° \\ \\ 70° = m\angle{4}[/tex]

As you can see, we plugged the x-value into the expression for the fourth angle because if you recall, you can tell that angles [tex]\displaystyle 1\:and\:4[/tex]are vertical angles, and accourding to the Vertical Angles Theorem, these angles are considered congruent, therefore seventy degrees is also the measure of the first angle.

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