The angles of a triangle are in AP. If the smallest angle is 36°, the

1.	The angles of a triangle are in AP. If the smallest angle is 36°, then the measure of the other angles are (A) 60°, 84° (B) 54°, 90°(C) 36°, 108° (D) 72°, 108°
Answer» (A) 60°, 84° Let the angles be x, x + d and x + 2d Given that x = 36° ∴ the angles are 36°, (36 + d)° and (36 + 2d)° Now, 36 + 36 + d + 36 + 2d = 180° ⇒ 3d = 72 ⇒ d = 24 ∴ The angels are (36 + 24)° and (36 + 48)° i.e. 60° and 84°

The angles of a triangle are in AP. If the smallest angle is 36°, then the measure of the other angles are (A) 60°, 84° (B) 54°, 90°(C) 36°, 108° (D) 72°, 108°

Answer»

(A) 60°, 84°

Let the angles be x, x + d and x + 2d

Given that x = 36°

∴ the angles are 36°, (36 + d)° and (36 + 2d)°

Now, 36 + 36 + d + 36 + 2d = 180°

⇒ 3d = 72

⇒ d = 24

∴ The angels are (36 + 24)° and (36 + 48)°

i.e. 60° and 84°