Question

One of the exterior angles of a triangle is 120° and the interior opposite angles of it are in the ratio 4 : 2. Find the angles of the triangle.

Answer 1

Step-by-step explanation:

Step-by-step explanation:

Exterior angle = 120° (given)

Interior opposite angles = 4 : 2

Let the common ratio be x.

So, interior opposite angles are 4x and 2x .

We know that,

By exterior angle property of a triangle

Exterior angle is equal to sum of interior opposite angles

⟹ 120° = 4x + 2x

⟹ 120° = 6x

⟹ 120°/6 = x

⟹ 20 = x

So, ∠ 1 = 4 × 20 = 80°

So, ∠ 2 = 2 × 20 = 40°