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Question
Lines AC and BD intersect at point P. m∠APD = 47°. Find the measures of ∠APB, ∠BPC, ∠CPD.
Solution
In the given figure,
∠DPA + ∠APB = 180∘ (Linear Pair angles)
⇒ 47∘ + ∠APB = 180∘
⇒ ∠APB = 133∘
Now,
∠APD = ∠BPC = 47∘ (Vertically opposite angles)
∠APB = ∠DPC = 133∘ (Vertically opposite angles)
Hence, the measures of ∠APB, ∠BPC, ∠CPD are 133∘, 47∘ and 133∘ respectively.
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