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Parallelogram

In the given ...

Question

In the given figure, AP and BP are angle bisectors of $∠$ A and $∠$ B respectively which meet at point P of the parallelogram ABCD. Then $2 ∠$ APB $=$ .

∠ A + ∠ B

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∠ A + ∠ C

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∠ B + ∠ D

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2 ∠ C + 3 ∠ B

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Solution

The correct option is C $∠ A + ∠ B$
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, $∠ A P B = 180 - (∠ 1 + ∠ 3) = 180 - (180 - (∠ 2 + ∠ 4)) = ∠ 2 + ∠ 4 = ∠ A / 2 + ∠ B / 2 \Rightarrow 2 ∠ A P B = ∠ A + ∠ B$

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In the given figure, AP and BP are angle bisectors of ∠A and ∠B respectively which meet at point P of the parallelogram ABCD. Then 2∠APB=.

The correct option is C ∠A+∠BIf AP and BP are angle bisector, then∠1=∠2=∠A/2∠3=∠4=∠B/2And Consecutive angles are supplementary ∴∠1+∠2=180−(∠3+∠4)∠A=180−∠BFrom the figure, ∠APB=180−(∠1+∠3)=180−(180−(∠2+∠4))=∠2+∠4=∠A/2+∠B/2⇒2∠APB=∠A+∠B

In the given figure, AP and BP are angle bisectors of $∠$ A and $∠$ B respectively which meet at point P of the parallelogram ABCD. Then $2 ∠$ APB $=$ .