In the following figure is AC || QR, then Y = ?
120°
In triangle PQR, point A lies on PQ and point C lies on PR, with AC drawn parallel to QR, so PR acts as a transversal cutting the two parallel lines AC and QR.
The angle marked 120° at C is the angle PCA, formed between CA and CP, on the side of the transversal facing P.
Since AC || QR, triangle PAC is similar to triangle PQR, and angle PCA corresponds to angle PRQ, so these corresponding angles are equal.
Angle y is the angle QRC, which is the same as angle PRQ since C lies on segment PR. Therefore y = angle PCA = 120°.
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