Question

The measure of two adjecent angles of a parallelogram are in the ratio 5:4. Find the measure of each of the angles of the parallelogram.​

Answer 1

Step-by-step explanation:

Let ∠A and ∠B are two adjacent angles.

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

∠A + ∠B = 180°

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

∠A+∠B=180°

5x+4x=180°

9x=180°

x=180/9

x=20°

∠A =5x=5×20=100°

∠B=4x=4×20=80°

Also, ∠B+∠C=180°[Since ∠B and ∠C are adjacent angles]

80°+∠C=180°

∠C=180°-80°=100°

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

100°+∠D=180°

∠D=180°-100°=80°

HOPE IT HELPS !!