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Question

In the figure, if PQRS, MXQ=135 and MYR=40. The measure of XMY is.

A
75
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B
40
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C
65
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D
85
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Solution

The correct option is D 85
Through point M, draw a line AB parallel to the line PQ.
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]

Also, XMY=XMB+BMY

XMY=45+40=85

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