Q8 of 25 Page 90

In ΔABC, the measure of angle A is equal to the sum of the measures of ∠B and ∠C. Also the ratio of measures of ∠B and ∠C is 4 : 5. Then find the measures of angles of the triangle.

Given that, In ΔABC


∠A = ∠B + ∠C eq.[1]


Let ∠B = x and ∠C = y


Then,


∠A = x + y


In ΔABC, By angle sum property of triangle


∠A + ∠B + ∠C = 180°


⇒ x + y + x + y = 180


⇒ 2x + 2y = 180


⇒ x + y = 90


⇒ x = 90 - y eq.[2]


Also, Given that




⇒ 5x = 4y


From eq.[2]


⇒ 5(90 - y) = 4y


⇒ 450 - 5y = 4y


⇒ 9y = 450


⇒ y = 50°


Putting this in eq.[2]


⇒ x = 90 - 50 = 40°


Therefore, we have


∠A = x + y = 40° + 50° = 90°


∠B = x = 40°


∠C = y = 50°


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