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Lines XY and CD intersect at M. If m∠XMC = 3x + 16 and m∠YMD = 5x - 54, find, in degrees, m∠CMY.

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Since XMC and YMD are vertical angles,
3x+16 = 5x-54
Solve for x, and you have their measures.
Now, since CMX and CMY are supplementary, CMX+CMY = 180

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