Q13 of 34 Page 170

In a triangle, each of the smaller angles is half the largest angle. Find the angles.

In a triangle ABC, let ∠C be the larger angle and ∠A and ∠B be the smaller ones. It is given that



⇒ 2∠A = 2∠B = ∠C


⇒ ∠A = ∠B


And ∠C = 2∠A


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


⇒ ∠A + ∠B + ∠C = 180°


⇒ ∠A + ∠A + 2∠A = 180°


⇒ 4∠A = 180 °


⇒ ∠A = 45°


So, ∠B = ∠A = 45°


∠C = 2× ∠A = 90°


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