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Question

In the figure, if PQRS, MXQ=135 and MYR=40, find XMY. [4 MARKS]


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Solution

Concept: 2 Marks
Application: 2 Marks

Through point M, draw a line AB parallel to the line PQ.



ABPQ and PQRS

QXM and XMB are interior angles on the same side of the transversal XM.

QXM+XMB=180 (Sum of the interior angles on the same side of transversal XM is supplementary)

135+XMB=180

XMB=180135=45

YMB=MYR=40 [alternate angles]

XMY=XMB+BMY

XMY=45+40=85


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