In ΔABC, ∠A = 2∠B and 2∠C = ∠A + ∠B. Find the angles.

1.	In ΔABC, ∠A = 2∠B and 2∠C = ∠A + ∠B. Find the angles.
Answer» ∠A + ∠B + ∠C = 180° …(i) (by angle sum property of a triangle) But ∠A + ∠B = 2∠C (given) 2∠C + ∠C = 180° ⇒ 3∠C = 180° ⇒ ∠C = 60° From (i), ∠A + ∠B + 60° = 180° ⇒ ∠A + ∠B = 120° But ∠A = 2 ∠B (given) 2∠B + ∠B = 120° ⇒ 3∠B = 120° ⇒ ∠B = 40° ∠A = 2 x 40 = 80° Hence angles of a ΔABC are 80°, 40°, 60°.

Answer»

∠A + ∠B + ∠C = 180° …(i) (by angle sum property of a triangle)

But ∠A + ∠B = 2∠C (given)

2∠C + ∠C = 180°

⇒ 3∠C = 180°

⇒ ∠C = 60°

From (i), ∠A + ∠B + 60° = 180°

⇒ ∠A + ∠B = 120°

But ∠A = 2 ∠B (given)

2∠B + ∠B = 120°

⇒ 3∠B = 120°

⇒ ∠B = 40°

∠A = 2 x 40 = 80°

Hence angles of a ΔABC are 80°, 40°, 60°.

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