Q6 of 34 Page 113

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

Given:

Let the angles are :


∠A = x, ∠B = x + 10, ∠ C = x + 20



As we know, using theorem (1), in any triangle, sum of the three interior angles is 180°.


So,


∠A + ∠B + ∠ C = 180°


⇒ x + x + 10 + x + 20 = 180°


⇒ 3x + 30° = 180°


⇒ 3x = 180° - 30°


⇒ 3x = 150°


⇒ x = 50°


So, the angles are,


∠A = x = 50°


∠B = x + 10 = 50° + 10° = 60°


∠ C = x + 20 = 50° + 20° = 70°


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