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

**Solution:**

Given, the figure represents an __isosceles trapezium__ ABCD.

AB||DC and AD = BC.

We have to find the value of x.

Given, ∠A = 60

We know that the angles opposite to the equal sides are equal.

Since AD = BC, ∠B = 60

Draw a line parallel to BC through D such that it intersects AB at E.

We observe that DEBC is a __parallelogram__.

So, BE = CD = 20 cm

DE = BC = 10 cm

We know that the __adjacent angles__ of a parallelogram are supplementary.

So, ∠DEB + ∠CBE = 180

∠DEB + 60 = 180

∠DEB = 180 - 60

∠DEB = 120

Consider triangle ADE,

Exterior angle, ∠ADE = 60

We know that the angles opposite to the equal sides are equal.

So, ∠DEA = 60

This implies ADE is an __equilateral triangle__.

Now, AE = 10 cm

x = AB

From the figure,

AB = AE + BE

= 10 + 20

= 30 cm

Therefore, the value of x is 30 cm.

**✦ Try This:** The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠DAC = 32° and ∠AOB = 70°, then ∠DBC is equal to?

**☛ Also Check: **NCERT Solutions for Class 8 Maths

**NCERT Exemplar Class 8 Maths Chapter 5 Problem 185**

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

**Summary:**

In the given figure, AB||DC and AD = BC. The value of x is 30 cm.

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