In the figure, if PQ∥RS,∠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 D85∘ 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)