Question

Given a trapezium ABCD in which AB || CD and AD = BC. If ∠C = 76°, then ∠D equals 

(a) 14°

(b) 104°

(c) 76°

(b) None of these

Answer 1

Correct option is (c) 76°

In trapezium ABCD, AB ∥ CD, AD = BC

Draw a perpendicular from A on CD to meet CD at M and a perpendicular from B on CD to meet at N.

Now, in △ADM and △BNC

∠AMD = ∠BNC (Each 90°)

AM = BN (distance between parallel lines)

AD = BC (Given)

Thus, △ADM ≅ △BCN (SAS rule)

Hence, ∠D = ∠C = 76^∘ (by CPCT)