The angles of a triangle are arranged in ascending order of magnitude. If the difference between two consecutive angles is 15°, find the three angles.

It is given that the angles of a triangle are arranged in ascending order of magnitude with the difference between consecutive angles = 15°.

So, the angles be x – 15°, x and x + 15°

We know that the sum of the angles of a triangle is 180°.

⇒ x – 15° + x + x + 15° = 180°

⇒ 3x = 180°

⇒ x = 60°

So, x – 15° = 60° - 15° = 45°

x + 15° = 60° + 15° = 75°