Question

One angle of a triangle is ${60}^{\circ }$. The other two angles are in the ratio of 5 :7. Find the two angles.

Answer 1

Step 1: Find the value of x

Given: ∠A = ${60}^{\circ }$ and ∠B:∠C=5:7

Let, ∠B = 5x, ∠C = 7x

⇒ ${60}^{\circ }$ + 5x + 7x = ${180}^{\circ }$ [∵ Angle sum property of triangle]

⇒ 12x = ${180}^{\circ }$- ${60}^{\circ }$

⇒ 12x = ${120}^{\circ }$

⇒ x = ${10}^{\circ }$

Step 2: Find the unknown angles:

∴ ∠B = 5x = ${50}^{\circ }$

⇒ ∠C = 7x = ${70}^{\circ }$

Hence, the two angles are ${50}^{\circ }$ and ${70}^{\circ }$.