An exterior angle of a triangle is 108° and its interior opposite angles are in the ratio 4 : 5. The angles of thetriangle are

The sum of the interior opposite angles of a triangle is equal to the exterior angle. In this case, the exterior angle is 108°.

The ratio of the two interior opposite angles is 4:5. This means that the angles can be represented as 4x and 5x.

Since the sum of these two angles is equal to the exterior angle, we can set up the following equation:

4x + 5x = 108

Solving for x gives:

x = 108 / 9 x = 12

Therefore, the two interior opposite angles are 4x = 48° and 5x = 60°.

The third angle of the triangle can be found by subtracting the sum of the two interior angles from 180° (since the sum of all angles in a triangle is 180°).

So, the third angle is 180 - 48 - 60 = 72°.

Therefore, the angles of the triangle are 48°, 60°, and 72°.