Question

One of the exterior angles of triangle is 160° and the interior opposite angles are in the ratio of 5 : 3. Find
the angles of the triangle.

Answer 1

Answer:

Let the angles be 5x and 3x

So 5x+3x=160(Sum of opposite interior angles)

x=20

Angles are 100 and 60

Answer 2

Answer:

Let the given interior opposite angles be is (5x)⁰ and (3x)⁰

We know that an exterior angle of a triangle is equal to the sum of its interior opposite angles.

therefore 5x+3x=160⁰

8x=160⁰

x=160/8

x=20

therefore angle A=5x=5×20=100⁰

angle B=3x=3×20=60⁰

But angle A+angle B+angle C=180⁰

therefore 100⁰+60⁰+angle C=180⁰

160⁰+angle C=180⁰

angle C=180⁰-160⁰

angle C=20⁰

angle A=100⁰, angle B=60⁰ , angle C=20⁰