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One of the angles of a triangle is three-fourth of sum of adjacent angles of parallelogram. Remaining angles of the triangle are in ratio 4 : 5 respectively. What is the value of smallest angle of the triangle?

One of the angles of a triangle is three-fourth of sum of adjacent angles of parallelogram. Remaining angles of the triangle are in ratio 4 : 5 respectively. What is the value of smallest angle of the triangle? Correct Answer 20° 

Sum of the adjacent angles of parallelogram = 180°

∴ First angle of the triangle = ¾ × 180° = 135°

∴ Sum of the remaining two angles = 180° - 135° = 45°

Ratio of the remaining two angles = 4 ∶ 5

∴ value of the second angle = (45° × 4)/(4 + 5) = 20°

∴ value of the third angle = (45° × 5)/(4 + 5) = 25°

∴ the smallest angle of the triangle = 20°

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