Question

Two opposite angles of a parallelogram are (3x – 2)° and (50 – x)°. Find the measure of each angle of the parallelogram .

Answer 1

We know that

Opposite sides of a parallelogram are equal

 ∴ 3x - 2 = 50 - x

⇒  3x + x = 50 + 2

⇒   4x = 52

⇒  x = 13°

∴(3x - 2)° = (3 × 13 - 2) = 37°

(50 - x)° = (50 -13°) = 37°

Adjacent angles of a parallelogram are supplementary

∴ x + 37 = 180°

∴ x = 180° - 37° = 143°

Hence, four angles are : 37°,143°, 37°,143°