Question

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

Answer 1

Let ABCD be a parallelogram.
∴ ∠​A = ∠​C and ∠B = ∠D (Opposite angles)
Let ∠A be the smallest angle whose measure is x^o.
∴​ ∠​B = (2x − 30)^o
Now, ∠​A + ∠B = 180^o (Adjacent angles are supplementary)
⇒ x + 2x − 30^o = 180^o
⇒ 3x = 210^o
⇒ x = 70^o
∴ ​∠​B = 2 ⨯ 70^o − 30^o = 110^o
Hence, ∠A = ∠C = 70^o; ∠B = ∠D = 110^o