Question

For triangle XYZ, m∠X = (2g + 16)° and the exterior angle to ∠X measures (4g + 38)°. Find the measure of ∠X and its exterior angle. Interior angle = 122°; exterior angle = 58° Interior angle = 58°; exterior angle = 122° Interior angle = 82°; exterior angle = 38° Interior angle = 38°; exterior angle = 82°

Answer 1

(b) Interior angle = 58°; exterior angle = 122°

Explanation:

Given a triangle's interior angle measures (2g+16)° and the adjacent exterior angle measures (4g+38)°, you want the measures of each of these angles.

Supplementary

An interior angle and its adjacent exterior angle are supplementary:

(2g +16)° +(46 +38)° = 180°

6g +54 = 180 . . . . . . . . . . . . . divide by °, collect terms

g +9 = 30 . . . . . . . . . . . divide by 6

g = 21 . . . . . . . . . subtract 9

X = (2·21 +16)° = 58°

The interior angle is 58°, and the exterior angle is 122°, matching choice B.

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