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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