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

see explanation

Step-by-step explanation:

the ratio of the opposite interior angles = 8 : 9 = 8x : 9x

The exterior angle of a triangle = sum of the opposite interior angles, hence

8x + 9x = 119

17x = 119 (divide both sides by 17)

x = 7

8 parts = 8x = 8 * 7 = 56

9 parts = 9x = 9 * 7 = 63

The sum of the 3 angles in a triangle = 180°

subtract the sum of the 2 angles from 180 for third angle in triangle

180° - (56 + 63) ° = 180° - 119° = 61°

The 3 angles of the triangle are 56°, 61°, 63°