Question

ABCD is a trapezium in which AB || DC and ∠A = ∠B = 45°. Then, ∠C = ______ and ∠D = ______.

Answer 1

Given:
ABCD is a trapezium
AB || DC
∠A = ∠B = 45°

Since, AB || DC
Thus, AD and BC are the transversals.
Therefore, sum of the interior angles must be equal to 180°.

∠A + ∠D = 180°
⇒ 45° + ∠D = 180°
⇒ ∠D = 180° − 45°
⇒ ∠D = 135°

∠B + ∠C = 180°
⇒ 45° + ∠C = 180°
⇒ ∠C = 180° − 45°
⇒ ∠C = 135°

Hence, ∠C = 135° and ∠D = 135°.