Question

prove that any adjacent angles of a parallelogram are supplementary

Answer 1

Solution :
D

Let ABCD is a parallelogram.

AE and AD is the bisector angles of adjacent angles of ∠A and ∠D.
As we know that,
∠A + ∠D = 180o (Sum of interior angles on the same side of traversal is 180o)
∠A + ∠D = 
= 90o ---------------(i)
Now, in triangle AOD,
∠AED + ∠A + ∠D = 180o (AE and AD is the angle bisector of ∠A and ∠D.)
∠AED + 90o = 180o (From eq (i))
∠AED = 180o - 90o = 90o
So, the bisectors of any two adjacent angles of a parallelogram intersect at 90o

Answer 2

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