Mathematics

Mathematics

Problem

In the given figure (not drawn to scale), ∠APO=42∘\angle APO = 42^\circ and ∠CQO=38∘\angle CQO = 38^\circ . Find the value of ∠POQ\angle POQ . ![A diagram showing three parallel lines A, M, and C, intersected by two transversals P and Q. Line A is labeled A and B (right arrow). Line M is labeled M and N (right arrow). Line C is labeled C and D (right arrow). Point P is on line A, and point Q is on line C. Point O is on line M. The angle between transversal P and line A, on the side of O, is labeled 1. The angle between transversal P and line M, on the side of O, is labeled 2. The angle between transversal P and line M, on the opposite side of O, is labeled 3. The angle between transversal Q and line C, on the side of O, is labeled 4. The angle POQ is the angle formed by transversals P and Q at point O.](https://storage.googleapis.com/diraq-contents/homework-question-parsing/marker/20260106T182719Z/6c76683f64f04c99b4b2693ee9b16082/935eed7aa61f7777f62cfc032e11bee9_img.jpg) A diagram showing three parallel lines A, M, and C, intersected by two transversals P and Q. Line A is labeled A and B (right arrow). Line M is labeled M and N (right arrow). Line C is labeled C and D (right arrow). Point P is on line A, and point Q is on line C. Point O is on line M. The angle between transversal P and line A, on the side of O, is labeled 1. The angle between transversal P and line M, on the side of O, is labeled 2. The angle between transversal P and line M, on the opposite side of O, is labeled 3. The angle between transversal Q and line C, on the side of O, is labeled 4. The angle POQ is the angle formed by transversals P and Q at point O. (A) 68∘68^\circ (B) 72∘72^\circ (C) 80∘80^\circ (D) 126∘126^\circ

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