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