Question

ABCD is a parallelogram such that its diagonals are equal. What is the measure of ∟ABC?

Answer 1

Answer:

L+A+B+C=360

that is your answer

Answer 2

Solution :-

ABCD is a parallelogram.

Therefore,

AB = CD , AD = BC

[ Opposite sides of parallelogram ]

Now, In ΔADB and ΔBCA

AD = BC

[ Opposite sides of parallelogram are equal ]

AC = DB [ Given , Diagonals of ||gm ]

AB = BA. [ Common ]

By SSS ,

ΔADB congruence to ΔBCA

By CPCT,

Angle DAB = Angle CBA. ( 1 )

Now , AD || BC

Therefore,

Angle DAB + Angle CBA = 180°

[ Opposite sides of parallelogram ABCD and transversal AB intersect then the sum of consecutive interior angles is equal to 180° ]

From ( 1 )

Angle CBA + Angle CBA = 180°

2AngleCBA = 180°

AngleCBA = 180° /2

Angle CBA = 90°

Now,

Angle CBA = 90°

Hence, Angle ABC = 90° $.$