The exterior angle of a triangle is 119° and its interior opposite angle are in the ratio 8:9. Find the angle of a triangle

Mathematics · High School · Tue Nov 03 2020

llm

Answered on Tue Jun 21 2022

We know, sum of two opposite interior angles is equal to exterior angle.

Then,

8x + 9x = 119°

17x = 119°

x = 119°/17

x = 7

So, angles are :

8x = 8 × 7 = 56°

9x = 9 × 7 = 63°

We know, sum of interior angles of triangle is 180°

Let C be third angle

So, 56° + 63° + C = 180°

119° + C = 180°

C = 180° - 119°

C = 61°

Hence, angles or triangle are 56°, 63° And 61°.