In the diagram, what is the measure of angle x?

Explanation

Use what you know about supplementary angles. At point Q, the 120° angle and ∠PQR are supplementary. That means the sum of their measures is 180°. So the measure of ∠PQR is 60°. At point R, the angles are also supplementary. So the measure of ∠PRQ is 30°. Now use the fact that the sum of the angles of any triangle is 180°.
m∠x m∠PQR m∠PRQ = 180°
m∠x 60° 30° = 180°
m∠x 90° = 180°
So m∠x = 180° – 90° = 90°.

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