Question

The angles of a traingle are in A.P and the ratio of greatest angle in radian to least angle in degree is π:60° Find angles in degrees​

Answer 1

The given ratio is π:60° = 180° : 60° = 3:1

So, the greatest and the smallest angles will be 3x and x respectively. Let the other angle be y.

Now, according to question,

3x, y, x will be in A.P. Remember, the order is much more important here, since 3x is the greatest angle and x is the smallest angle, so y has to be in between 3x and x.

This implies, 3x + x = 2y => 2x = y

The given angles boils down to 3x, 2x and x.

Using angle sum property of a triangle,

3x + 2x + x = 180° => x = 30°

Thus, the angles are 90°, 60°, and 30°.

Hope it'll help you.....