Find the measure of each angle of a parallelogram, if one of its angles is 30° less than twice the smallest angle.

Question

Find the measure of each angle of a parallelogram, if one of its angles is 30&#xB0; less than twice the smallest angle.

Philoid · Accepted Answer

Let ABCD be the parallelogram.

We know that opposite angles of parallelogram are equal.

∴∠A = ∠C and ∠B = ∠D
Let ∠A be the smallest angle whose measure is x°.
∴ ∠B = (2x − 30)°
We know that adjacent angles of parallelogram are supplementary,

∠A + ∠B = 180°
x + 2x − 30° = 180°
3x = 210°
x = 70°
∴ ∠B = 2 ⨯ 70° − 30° = 110°
Hence, ∠A = ∠C = 70° and ∠B = ∠D = 110°