AB ∥ CD and a transversal cuts AB at P and CD at Q, with ∠APQ = (5x − 8)° and ∠PQD = (3x + 24)°. The bisector of ∠BPQ meets CD at R. Find ∠PRQ.

Question

Accepted Answer

54°. ∠APQ and ∠PQD are alternate angles, so 5x - 8 = 3x + 24, x = 16 and ∠APQ = 72°. Then ∠BPQ = 108° and its bisector makes ∠BPR = 54°. ∠PRQ and ∠BPR are alternate angles, so ∠PRQ = 54°.

AB ∥ CD and a transversal cuts AB at P and CD at Q, with ∠APQ = $(5 x - 8)$ ° and ∠PQD = $(3 x + 24)$ °. The bisector of ∠BPQ meets CD at R. Find ∠PRQ.

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More Geometry practice

AB ∥ CD and a transversal cuts AB at P and CD at Q, with ∠APQ = (5x−8)° and ∠PQD = (3x+24)°. The bisector of ∠BPQ meets CD at R. Find ∠PRQ.

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Geometry practice

AB ∥ CD and a transversal cuts AB at P and CD at Q, with ∠APQ = $(5 x - 8)$ ° and ∠PQD = $(3 x + 24)$ °. The bisector of ∠BPQ meets CD at R. Find ∠PRQ.