Question

Find the measure of GTR

Answer 1

`\displaystyle 68° = m\angle{GTR}`

Explanation:

`\displaystyle [5f + 83]° = [4f + 80]° \hookrightarrow (3)/(-1) = (-f)/(-1) \\ \\ -3 = f \\ \\ \\ [4[-3] + 80]°; [-12 + 80]° \\ \\ 68° = m\angle{FTH}`

As you can see, we plugged the m-value into the expression for angle
`\displaystyle FTH`because if you recall, you can tell that angles
`\displaystyle FTH\:and\:GTR`are vertical angles, and accourding to the Vertical Angles Theorem, these angles are considered congruent, therefore sixty-eight degrees is also the measure of angle
`\displaystyle GTR.`

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