Class 8 CH. 3 ex 3.3 Q.no. 5

Q5 :
The measures of two adjacent angles of a parallelogram are in the ratio 3:2. Find the
measure of each of the angles of the parallelogram.
Answer :
Let the measures of two adjacent angles, ∠A and ∠B, of parallelogram ABCD are in the ratio of
3:2. Let ∠A = 3x and ∠B = 2x
We know that the sum of the measures of adjacent angles is 180 º for a parallelogram.
∠A + ∠B = 180 º
3x + 2x = 180 º
5x = 180 º
X=180/5=36
∠A = ∠C = 3x = 108 º (Opposite angles)
∠B = ∠D = 2x = 72 º (Opposite angles)

Thus, the measures of the angles of the parallelogram are 108 º, 72 º, 108 º, and 72 º.