Question

In the following figure, AB || DC and AD = BC. Find the value of x.

Answer 1

Given: An isosceles trapezium, AB || DC, AD = BC and ∠A = 60°.

So, ∠B = 60°.

Construction: Draw a line parallel to BC through D.

Now, DEBC is a parallelogram,

BE = CD = 20 cm and DE = BC = 10 cm.

Now, ∠DEB + ∠CBE = 180°   ...[Adjacent angles are supplementary in parallelogram]

∠DEB = 180° – 60°

∠DEB = 120°

In triangle ADE,

∠ADE = 60°   ...[Exterior angle]

Also, in triangle ADE is an equilateral triangle.

AE = 10 cm

AB = AE + EB

AB = 10 + 20

AB = 30 cm

Hence, x = 30 cm.