Question

In trapezium ABCD, AB║DC. If ∠D=x° then ∠A = __________.Fill in the blank.

Answer 1

According to the question there is a trapezium ABCD where AB is parallel to DC and ∠D is x°. Therefore it is an isosceles trapezium. Not only this but also the angles on either side of the bases are the same.

Therefore adjacent angles along the sides are supplementary.

i.e. ∠D + ∠A = 180

Therefore, x° + ∠A = 180

or, ∠A = 180 - x (Ans)

Answer 2

let ABCD is a trapezium in such a way that AB || DC and ∠D = X° as shown in figure.AB || DC ,so, the interior angles on the same side of the transversal are supplementary.

e.g., ∠D + ∠A = 180° and ∠C + ∠B = 180°

now, ∠A = 180° - ∠D

= 180° - X° = (180 - X)°

hence, ∠A = (180 - X)°