Question

one of the exterior angles of a triangle is 153° and the interior opposite angles are in the interior opposite angles are in the ratio 5:4 . find the three interior angles of the triangle.​

Answer 1

Answer:

Three interior angles are : 27°, 68° and 85°

Step-by-step explanation:

Let the interior angles opposite to exterior angle be 5x and 4x, where x is a common factor

Sum of 2 interior angles = Opposite exterior angle ( Formula )

5x + 4x = 153°

=> 9x = 153

=> x = 153/9 = 17°

So the 2 interior angles are : 5x = 5(17) = 85° and 4x = 4(17) = 68°

Now, sum of 3 interior angles of a traingle = 180°

=> 3rd angle = 180° - ( 85+68)

=> 3rd angle = 180° - 153° = 27°