Question

Find the measure of angle 1

Answer 1

`\displaystyle 70° = m\angle{1}`

Explanation:

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

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

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
`\displaystyle 1\:and\:4`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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