Question

- In the adjoining figure, ABCD is a parallelogram and angle A = 120°. If the
bisectors of angle A and angle B meet at a point P, show that angle APB is a right
angle.
[Hint : Since angleA = 120°, so angle B = 60° (Why?)
.. angle PAB = 60° and angle ABP = 30° (Why?)]​

Answer 1

Answer:

If AP and BP are angle bisector, then

∠1=∠2=∠A/2∠3=∠4=∠B/2

And Consecutive angles are supplementary

 ∴∠1+∠2=180−(∠3+∠4)

∠A=180−∠B

From the figure, ∠APB=180−(∠1+∠3)=180−(180−(∠2+∠4))=∠2+∠4=∠A/2+∠B/2⇒2∠APB=∠A+∠B

Step-by-step explanation:

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