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Question
The consecutive angles of a parallelogram are in the ratio 3:6. Calculate the measures of all the angles of the parallelogram.
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Solution
Let ABCD is a parallelogram in which AD || BC.
∠A and ∠B are consecutive angles:
∠A : ∠B = 3 : 6
∴ ∠A = 3x and ∠B = 6x
AD || BC and AB is the transversal.
⇒ ∠A + ∠B = 180° ....(Co-interior angles are supplementary)
⇒ 3x + 6x = 180°
⇒ 9x = 180°
⇒ x = 20
∴ ∠A = 3 x 20° = 60° and ∠B = 6 x 20° = 120°
Since opposite angles of a parallelogram are equal.
∴ ∠C =∠A = 60° and ∠D = ∠B = 120°.
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