Question

One of the Exterior angles of a triangle is 120 degrees and the interior opposite angles in the ratio 1:2 Find the angles of the Triangles ..With steps pls

Answer 1

Answer:

Angles are 40°, 60° and 80°.

Step-by-step explanation:

Ratio of interior angles = 1:2

Let interior opposite angles be x and 2x.

Now we know that sum of interior opposite angles in a triangle is equal to exterior angle of triangle.

=> x + 2x = 120°

=> 3x = 120°

∴ x = 120°/3 => 40°

∴ 2x = 2(40) => 80°

To find third angle, we use ASP (Angle Sum Property) of triangle.

Let third angle be y.

By ASP of triangle,

40° + 80° + y = 180°

=> 120° + y = 180°

∴ y = 180° - 120° => 60°

Thus, the angles of the triangle are 40°, 60° and 80°.