Question

The three angles of a triangle are in AP. Find the angles if the greatest angle is three times smallest​

Answer 1

$\sf { \underline{SOLUTION}}$

GIVEN

• The three angles of a triangle are in AP.

• The greatest angle is three times smallest

TO DETERMINE

The angles

EVALUATION

Since the angles are in AP

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

Since in a triangle sum of the three angles is 180°

x + (x+d) + (x+2d) = 180°

→ 3x+3d= 180°

∴ x + d = 60°

Again by the given condition

x + 2d = 3x

→ 2d = 2x

→ d = x

So

x+d = 60° gives

2x = 60°

→ x = 30°

So d = 30°

FINAL ANSWER

The required angles are 30°, 60° , 90°

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