An exterior angle of a triangle measures 110° and its interior opposite angles are in the ratio 2: 3. Find the angles of the triangle.

Let the given interior opposite angles are (2x) and (3x). 

An exterior angle of a triangle is equal to the sum of its interior opposite angles. 

2x + 3x = 110 

= 5x = 110 

= x = 110 / 5 

= x = 22 

∠A = 2x = 2 × 22 = 44 

∠B = 3x = 3 × 22 = 66 

But, ∠A + ∠B + ∠C = 180 

∴ 44 + 66 + ∠C = 180 

= 110 + ∠C = 180 

= ∠C = 180 – 110 

= ∠C = 70 

∴∠A = 44, ∠B = 66, ∠C = 70

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