# 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

2A = 2B = C

⇒ ∠A = B

And C = 2A

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

⇒ ∠A + B + C = 180°

⇒ ∠A + A + 2A = 180°

4A = 180 °

⇒ ∠A = 45°

So, B = A = 45°

C = 2× A = 90°

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