Question

One angle of a triangle is 60°. The other two angles are in the ratio of 5: 7. Find the two angles.

Answer 1

In Δ ABC,

Let ∠A = 60° and then ∠B: ∠C = 5: 7
But ∠A + ∠B + ∠C = 180° ........(Angles of a triangle)

⇒ 60° + ∠B + ∠C = 180°

⇒ ∠B + ∠C = 180°− 60° = 120°

Let ∠B = 5x and ∠C = 7x

∴ 5x + 7x = 120°

⇒ 12x = 120°

⇒ x =`(120°)/12=10°`

∴ ∠B = 5x = 5 × 10° = 50°

∠C = 7x = 7 × 10° = 70°