Question

ABCD is a parallelogram. AE = BE.
Find the value of x.

Answer 1

Answer:

x=60°

Step-by-step explanation:

Solution :

In ΔAEB,

AE = BE ...(Given)

∠EAB=∠EBA ...(Isosceles triangle theorem)

∴EBA = 50°

Now,

In □ABDC,

∠ABE+∠EBD = ∠ABD ...(Angle Addition Postulate)

∴∠ABD = 50+20 = 70°

And

∠CAE+∠BAE= ∠CAB ...(Angle Addition Postulate)

∴∠CAB = (x+50)°

Now,

AC || BD ...(Opposite sides of a parallelogram are parallel)

Hence,

∠CAB+∠ABD = 180° ...(Interior angle theorem)

∴x+50+70=180

∴x=60°