SSC MTS Model Paper 3

Question : 45 of 150

Marks: +1, -0

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

$11{π/24}$
$π/12$
$π/24$
$5π/24$

Validate

Solution:

Decreased angles be 2x°, 3x°, 5x°
∴ Real angles would be
(2x + 15)°, (3x + 15)°, (5x + 15)°
⇒ 2x + 15 + 3x + 15 + 5x + 15 = 180
⇒ 10x + 45 = 180 ⇒ 10x = 135

x = { 135 }/ { 10 }

∴ Greatest angle = (5x + 15)°

= ( 5 × { 135 } /{ 10 } + 15 t) ^ { ° }

= ( { 135 } /{ 2 } + 15 ) ^ { °} = ( { 165 }/ { 2 } ) ^ { }

∴

The radian measure

= ( { 165 } /{ 2 } ) ^ { ° } × { π }/ { 180 ^ { ° } } = { 11 }/ { 24 }π

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