Question

Two adjacent angles of a parallelogram are in the ratio 4:5. Find the measure of each of its angles.

Answer 1

Let ∠A and ∠B are two adjacent angles.

But we know that sum of adjacent angles of a parallelogram is 180^o

∠A + ∠B = 180^o

Given that adjacent angles of a parallelogram are in the ratio 4:5 and let that ratio be multiple of x

∠A + ∠B = 180^o

4x + 5x = 180^o

9x = 180^o

x = 180/9

x= 20^o

∠A = 4x = 4 × 20 = 80^o

∠B = 5x = 5 × 20 = 100^o

Also ∠B + ∠C = 180^o [Since ∠B and ∠C are adjacent angles]

100^o+ ∠C = 180^o

∠C = 180^o– 100^o= 80^o.

Now ∠C + ∠D = 180^o [Since ∠C and ∠D are adjacent angles]

80^o+ ∠D = 180^o

∠D = 180^o– 80^o= 100^o