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

Open in App

Solution

For the given parallelogram ABCD,
m $∠$ B = (3x – 2)°, m $∠$ = (50 – x)°
(3x – 2)° = (50 – x)° (Opposite angles of a parallelogram are congruent)
4x = 52
x = 13
So, the measures of the different angles are
m $∠$ D = (50 – x)° = (50 – 13)° = 37°
m $∠$ B = 37°
m $∠$ A + m $∠$ D = 180° (Sum of adjacent angles of a parallelogram is 180°)
m $∠$ A = 143°
m $∠$ C = m $∠$ A (Opposite angles of a parallelogram are congruent)
∴ m $∠$ A = m $∠$ C = 143°
m $∠$ B = m $∠$ D= 37°

Suggest Corrections

Similar questions

{(3 x - 2)}^{\circ}

{(50 - x)}^{\circ}

{(3 x - 2)}^{o}

{(50 - x)}^{o}

(3 x - 2)

(x + 48)

Join BYJU'S Learning Program