Question

The angles of a triangle are arranged in descending order of their magnitudes. If the difference between two consecutive angles is 10°, find the three angles.

Answer 1

Let one of the angles of a triangle be x. If angles are arranged in descending order. Then, angles will be x, (x – 10°) and (x – 20°).

We know that the sum of all angles in a triangle is equal to 180°

So, x + (x – 10°) + (x – 20°) = 180°

⇒ x + x + x – 30° = 180°

⇒ 3x = 180° + 30°

⇒ 3x = 210°

⇒ x = `210^circ/3` = 70°

Hence, angles will be 70°, 70° – 10° and 70° – 20° i.e., 70°, 60° and 50°.