Question

prove that the bisectors of two adjacent angles of a parallelogram enclose a right angle.
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Answer 1

Answer:

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Answer 2

Given :-

ABCD is a parallelogram such that angles bisectors of adjacent angles A and angle B intersect at point P.

To prove :-

∠APB = 90°

PROOF :

∠BAD + ∠ABC = 180°

[ ∴ AD║BC and ∠BAD and ∠ABC are consecutive interior angles ]

Now,  

[ ∴ Sum of interior angles of triangle ]

⇒ 90° + ∠APB = 180°

⇒ ∠APB = 180° - 90°

∴ ∠APB = 90°

Hence  Proved.

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