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Question
PQ = PR, PS || QR, ∠SPR = 72. ∴ find ∠QPR.
Options
72°
18°
44°
36°
MCQ
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Solution
36°
Explanation:
Since PQ = PR (given), triangle PQR is isosceles and therefore:
- ∠PQR = ∠PRQ (base angles of an isosceles triangle).
Given that ∠SPR = 72° and considering the parallel lines PS || QR, we know the corresponding angles between parallel lines give us:
- ∠SPR = ∠QPR (because PS is parallel to QR).
Thus, ∠QPR = 36°, which is half of ∠SPR.
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