Question

The opposite angles of a parallelogram are (3x – 2)° and (x + 48)°. Find the measure of each angle of the parallelogram.

Answer 1

Opposite angles of a parallelogram are given. 

They are (3x – 2)°, (x + 48)°

⇒ 3x – 2 = x + 48° [ ∵ opposite angles of a parallelogram are equal] 

⇒ 3x – x = 48 + 2 => 2x = 50 

∴ x = 25°

A = 3x – 2° = 3 x 25° -2° = 75° -2° = 73° 

∠A = ∠C = 73°

∠B = 180° – ∠A [ v adjacent angles of a parallelogram are supplementary] 

= 180° – 73° = 107° 

∴ ∠B = ∠D = 107°