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