Question

Lines AC and BD intersect at point P. m∠APD = 47°. Find the measures of ∠APB, ∠BPC, ∠CPD.

Answer 1

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.