Question

P is a point on the side AD of the square ABCD such that Z CPD = 30°. CP and diagonal BD intersect each other at the point 0. The measure of 2 COD is (a) 60° (b) 45° (c) 75° (d) 30°​

Answer 1

Answer:

In square ABCD,

OB=BP (Given)

∴∠DPB=∠BOP [Angular opposite to equal sides]

∠DPB=290∘=45∘

∠BOP=2180∘−45∘=67.5∘

∠BOC=90∘ [Diagonal bisect at right angle]

∠POC=90∘−67.5∘=22.5∘

△BDC is an isosceles  △ , with  ∠BDC=90∘  & ∠BDC=∠DBC=45∘

Therefore,  ∠BDC=2∠POC

Hence statement is true.

Step-by-step explanation:

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