Q4 of 59 Page 63

ABCD is a parallelogram. The ratio of ∠A and ∠B of this parallelogram is 5 : 4. Find the measure of ∠B.

Given: ∠A : ∠B = 5:4

Let the measure of ∠A = 5x


Then ∠B = 4x


Since the adjacent angles of a parallelogram are complementary, therefore ∠A + ∠B = 180°


⇒ 5x + 4x = 180°


⇒ 9x = 180°


⇒ x = 20°


∴ ∠ A = 5x = 5 × 20° = 100°


∴ ∠ B = 4x = 4 × 20° = 80°


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