# 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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