​ BCD is a trapezium in which AB||DC If ∠A = ∠B =30°, what are the measures of the other two angles? ​

Question

BCD is a trapezium in which \(\overline{AB}||\overline{DC}\) If ∠A = ∠B =30°, what are the measures of the other two angles?

Answer 1

Given : ABCD is a trapezium.

∠A = ∠B = 30°

Since AB//CD,

∠A + ∠D = ∠B + ∠C = 180° (interior angles on the same side of a
transversal are supplementary)

30° + ∠D = 180°

∠D = 180° – 300°

= 150°

and 30° + ∠C = 180°

∠C = 180° – 30’

= 150°