Lines AB and CD are parallel, with A and C to the left of the transversal XY, and B and D to the right. The transversal intersects AB at M and CD at N, where X, M, N, and Y are collinear in that order. If measure of ∠XMA=125°, then the measure of ∠CNY is:
55°
Since AB ∥ CD and XY is a transversal cutting AB at M and CD at N, the angle ∠XMA at M and the angle ∠MNC at N are corresponding angles (both are on the left side of the transversal, above their respective lines from N's viewpoint).
By the corresponding angles postulate, \(\angle MNC = \angle XMA = 125°\).
At point N, the angles ∠MNC and ∠CNY form a linear pair along the straight line XY, so \(\angle MNC + \angle CNY = 180°\).
Therefore, \(\angle CNY = 180° - 125° = 55°\).
Hence, the measure of ∠CNY is 55°.
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