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The complement of an angle and the supplement of the same angle are in the ratio 2 : 7. Find the angle (in degrees).

Class 9Pairs of AnglesGeometry — Lines and Angles

A54
B59
C49
D108

Step-by-Step Solution

Let the angle be

x . \frac{90 - x}{180 - x} = \frac{2}{7}

. Cross-multiply:

7 (90 - x) = 2 (180 - x), 630 - 7 x = 360 - 2 x, 270 = 5 x, x = 54

deg.

Answer: A) 54

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