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