The sides AB and CD of a quadrilateral ABCD are extended to points P and Q respectively. Is ∠ADQ + ∠CBP = ∠A + ∠C? Give reason
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Join AC, then
∠CBP = ∠BCA + ∠BAC and
∠ADQ = ∠ACD + ∠DAC
(Exterior angles of triangles)
Therefore, ∠CBP + ∠ADQ = ∠BCA + ∠BAC + ∠ACD + ∠DAC
= (∠BCA + ∠ACD) + (∠BAC + ∠DAC)
= ∠C + ∠A
Hope it helps!
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