Question

In the given figure, ABCD is a parallelogram. P is the midpoint of CD and CD = 2BC. Find the measure of <APB.​

Answer 1

Answer:

Correct option is A)

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

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⇒2∠ADP+∠DAP=180

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

In parallelogram ABCD ∠DAP+∠CBP=180

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

Then ∠DPA+∠CPB=90

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Then ∠DPA+∠CPB+∠DPC=180

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⇒∠DPC=180−90=90

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