In the figure, QRST is a rectangle; PT// QM, angle P = 60o. Find angle MUR

In the figure, QRST is a rectangle; PT// QM, angle P = 60o. Find angle MUR

Mathematics

JAMB 1982

In the figure, QRST is a rectangle; PT// QM, angle P = 60o. Find angle MUR

A. 150^o
B. 30^o
C. 60^o
D. 120^o
E. 90^o

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Correct Answer: Option A

Explanation

In the given figure, QRST is a rectangle with PT parallel to QM and ∠TPQ = 60°.
Since PT ∥ QM, and PQ is a transversal, the corresponding angle ∠PQM = 60°, so the remaining angle ∠MQR = 90° − 60° = 30°.
Therefore, ∠MUR (the angle formed by the line from M through U to R) is supplementary to this 30° angle, making it 180° − 30° = 150°

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