Question

One of the exterior angle of a triangle is 120
 and its interior opposite angles are in the ratio 5 : 3. Find all the angles of the triangle.​

Answer 1

Step-by-step explanation:

Exterior angle = 120° (given)

Interior opposite angles = 2: 3

Let the common ratio be x.

So, interior opposite angles are 2x and 3x .

We know that,

By exterior angle property of a triangle

Exterior angle is equal to sum of interior opposite angles

⟹ 120° = 2x + 3x

⟹ 120° = 5x

⟹ 120°/5=x

⟹ 24=x

So, ∠ 1 = 2 × 24 = 48°

So, ∠ 2 = 3 × 24 =72°