Q4 of 34 Page 113

The angles of a triangle are in the ratio 1:2:3. Determine the three angles.

Given: the ratio of angles as 1:2:3

So, let the angle,


∠A = x, ∠B = 2x, ∠ C = 3x



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


So,


∠A + ∠B + ∠ C = 180°


⇒ x + 2x + 3x= 180°


⇒ 6x = 180°


⇒ x = 30°


So, the angles are,


∠A = x = 30°


∠B = 2x = 2 × 30° = 60°


∠ C = 3x = 3 × 30° = 90°


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