Question

In ∆ABC, the measure of ∠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

Answer 1

Let the measure of ∠B be ‘x°’ and that of ∠C be ‘y°’. 

According to the first condition,

m∠A = m∠B + m∠C 

∴ m∠A = x° + y° 

In AABC, 

m∠A + m∠B + m∠C = 180° …[Sum of the measures of the angles of a triangle is 180°] 

∴ x + y + x + y = 180 ,

∴ 2x + 2y = 180 

Dividing both sides by 2,

 x + y = 90 …(i)

According to the second condition, 

he ratio of the measures of ∠B and ∠C is 4 : 5. 

∴ x/y = 4/5

∴ 5x = 4y 

∴ 5x – 4y = 0 …….(ii)

 Multiplying equation (i) by 4,

4x + 4y = 360 …(iii) 

Adding equations (ii) and (iii),

∴ x = 40 

Substituting x = 40 in equation (i),

 x + y = 90 

∴ 40 + y = 90 

∴ y = 90 – 40 

∴ y = 50 

∴ m∠A = x° + y° = 40° + 50° = 90° 

∴ The measures of ∠A, ∠B and ∠C are 90°, 40°, and 50° respectively.