find the measure of each angle of a parallelogram, if one of its angle is 30 degree less than twice of the smallest angle.

Lalit Mehra , Meritnation Expert added an answer, on 9/3/11

Hi!

Here is the answer to your question.

Let ∠A be the smallest angle of the parallelogram ABCD

∠A = ∠C (opposite angles of parallelogram are equal)

∠B = ∠D (opposite angles of parallelogram are equal)

Given, ∠B = 2∠A – 30°

∠A + ∠B = 180° (sum of consecutive interior angles is supplementary)

⇒ ∠A + (2∠A – 30°) = 180°

⇒ 3∠A = 210°

⇒∠A = 70

∴∠B = 2 × 70° – 30° = 140° – 30° = 110°

Thus, ∠A = ∠C = 70° and ∠B = ∠D = 110°

Cheers!

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