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Q. 84.5( 41 Votes )

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.

Class 9th MHB - Math Part-I 5. Linear Equations in Two Variables

Answer :

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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