Question

Two adjacent angles of a parallelogram are in the ratio 2: 3, the measure of angles will be

• A. 90^o, 90^o, 90^o, 90^o
• B. 72^o, 108^o, 72^o, 108^o
• C. 70^o, 110^o, 70^o, 110^o
• D. 80^o, 100^o, 80^o, 100^o

Answer 1

The correct option is B

72^o, 108^o, 72^o, 108^o

Let adjacent angles ∠A and ∠D be 2x and 3x.

AB || DC and AD is a transversal, then 2x + 3x = 180^o

(angles on same side of transversal)

x = 36^o.

So, ∠A = 72^o, ∠D = 108^o.

Thus ∠B = ∠D =108^o, and ∠A = ∠C = 72^o

(opposite angles of parallelogram are equal).