Question:
Two opposite angles of a parallelogram are (3x - 2)° and (50 - x)°. Find the measure of each angle of the parallelogram.
Solution:
We know that,
Opposite sides of a parallelogram are equal.
(3x - 2)° = (50 - x)°
⟹ 3x + x = 50 + 2
⟹ 4x = 52
⟹ x = 13°
Therefore, (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°.