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

Question

An exterior angle of a triangle is 108&#xB0; and its interior opposite angles are in the ratio 4 : 5. The angles of the triangle are

Philoid · Accepted Answer

Let ∠1, ∠2 and ∠3 be the angles of the triangle and ∠4 be its exterior angle.

∠4 = 108⁰ (Given)

∠1: ∠2 = 4: 5 (Given)

Let, ∠1 = 4k

∠2 = 5k

Now,

∠1 + ∠2 = 108^o (Exterior angle theorem)

4k + 5k = 108^o

9k = 108^o

k = 12^o

Thus,

∠1 = 4 * 12 = 48^o

∠2 = 5 * 12 = 60^o

We know that,

∠1 + ∠2 + ∠3 = 180^o

48^o + 60^o + ∠3 = 180^o

108^o + ∠3 = 180^o

∠3 = 180^o – 108^o

= 72^o

Thus, angles of triangle are 48^o, 60^o, 72^o.