Question

Two unequal angles of a parallelogram are in the ratio 2 : 3. Find all its angles in degrees .

Answer 1

Let `∠`A = 2x and `∠`B = 3x

Now,

`∠`A + `∠`B = 180°                           [Co-interior angles are supplementary]

2x + 3x -180°                              [ AD || BC and AB is the transversal]

⇒ 5x =180°

⇒ x = `(180°)/ 5` = 36°

∴`∠`A = 2 ´ 36° = 72°

`∠` B = 3´ 36° = 108°

Now,

`∠`A = `∠`C = 72°                           [Opposite side angles of a parallelogram are equal]

`∠`B = `∠`D =108°