Question

ABCD is a parallelogram as shown in the
figure. If AB = 2AD and P is the mid-point
of AB, what is the measure of angle CPD ?

A) 90° (B) 60°
(B) 60° (C) 45°
(D) 135°

Plz provide step by step solution
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Answer 1

Answer:

Given AB=2 AD and P is the mid point of AB then

AP=AD And PB=BC because opposite side of parallelogram are equal

In ΔDAP,∠ADP=∠DPA

So ∠ADP+∠DPA+DAP=180

0

⇒2∠ADP+∠DAP=180

Similarlyin\Delta PBC ,2\angleCPB+CBP=180^{0}$$

In parallelogram ABCD ∠DAP+∠CBP=180

0

Then 2\angle ADP+\angle DAP+,2\angleCPB+CBP=180+180

Then ∠DPA+∠CPB=90

0

Then ∠DPA+∠CPB+∠DPC=180

0

⇒∠DPC=180−90=90

0

Step-by-step explanation:

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