Can a quadrilateral ABCD be a parallelogram if
$∠ D + ∠ B = 180^{o}$ ?

Open in App

Solution

If in a quadrilateral ABCD, $∠ D + ∠ B = 180^{o}$ , then it is not necessary that ABCD is a parallelogram.

As, opposite angles of parallelograms are congruent. Consecutive angles are supplementary. If one angle is right, then all angles are right. The diagonals of a parallelogram bisect each other.

So, $∠ D + ∠ B = 180^{o}$ is not necessary to be ABCD is a parallelogram.

Suggest Corrections

Similar questions

∠ A = 70^{o}

∠ C = 65^{o}

∠ D + ∠ B = 180^{\circ}

Let ABCD be a quadrilateral in which ∠A = ∠C, and ∠B = ∠D. Prove that ABCD is a parallelogram.

Can a quadrilateral ABCD be a parallelogram if

(i) ∠D + ∠B = 180°?

(ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?

(iii) ∠A = 70° and ∠C = 65°?

∠ D + ∠ B = 180^{0}

1

0

Join BYJU'S Learning Program