By decreasing 15° of each angle of a triangle, the ratios of their angles are 2:3:5, The radian measure of greatest angle is : ?->(Show Answer!)

1. By decreasing 15° of each angle of a triangle, the ratios of their angles are 2:3:5, The radian measure of greatest angle is :

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By: anil on 05 May 2019 01.59 am

After decreasing 15° from each angle of triangle let the values of corresponding angles be 2x, 3x and 5x so that their ratio would be 2x:3x:5x or 2:3:5.
Thus the value of angles of triangle must be (2x + 15°), (3x + 15°) and (5x + 15°).
We know that,
Sum of angles of triangle = 180°
∴(2x + 15°) + (3x + 15°) + (5x + 15°) = 180°
10x + 45° = 180°
x = 13.5°
Hence, the value of the greatest angle of triangle = 5x + 15° = 5 × 13.5 + 15 = 82.5°
= $$frac{82.5}{180}$$ π
=11π/24 Hence, the radian measure of greatest angle is 11π/24

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