Question

An exterior angle of a triangle is 108° and its interior opposite angles are in the ratio 4 : 5. The angles of the triangle are

Options

• 48°, 60°, 72°

•  50°, 60°, 70°

• 52°, 56°, 72°

• 42°, 60°, 76°

Answer 1

In the given ΔABC, an exterior angle  ∠ADC = 108° and its interior opposite angles are in the ratio 4:5.

Let us take,

∠A = 4x

∠B = 5x

Now using the property, “exterior angle of a triangle is equal to the sum of two opposite interior angles”

We get,

∠A + ∠B = 108°

  4x + 5x = 108°

          9x = 108°        

         `x = (108°)/ 9`

          x  = 12

Thus, 

∠A = 4x = 4(12°) = 48°

∠B = 5x = 5(12°) = 60°

Also, using angle sum property in ΔABC

∠A + ∠B + ∠C = 180°

48° + 60° + ∠C = 180°

108° + ∠C = 180°

∠C = 180° - 108°

∠C = 72°

Thus, 

∠A = 48°

∠B = 60°

∠C = 72°