Question

One angle of a triangle is 61° and the other two angles are in the ratio `1 1/2: 1 1/3`. Find these angles.

Answer 1

In Δ ABC,
Let ∠A = 61°
But ∠A + ∠B + ∠C = 180° ........(Angles of a triangle)

⇒ 61° + ∠B + ∠C = 180°

⇒ ∠B + ∠C = 180°− 61° = 119°

But ∠B: ∠C =`1 1/2:1 1/3=3/2:4/3`

`=(9:8)/6`

=9: 8

Let ∠B = 9x and ∠C = 8x,
then, 9x + 8x = 119°

⇒ 17x = 119°

⇒ x =`(119°)/17=7°`

∴ ∠B = 9x = 9 × 7° = 63°
∠C = 8x = 8 × 7° = 56°