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Question

# The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. Find the difference between the measure of the largest angle and the smallest angle.

A

36°

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B

108°

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C

72°

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D

144°

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Solution

## The correct option is B 108° Given that the angles of a quadrilateral are in the ratio 1 :2 :3 : 4. Let the angles be x , 2x, 3x and 4x. The sum of angles of a quadrilateral is 360°. Hence we have x + 2x+ 3x + 4x = 360° 10x = 360° Hence, x = 36° The measure of the smallest angle = 36° The measure of other angles are: 2×36∘=72∘ 3×36∘=108∘ 4×36∘=144∘ The measure of the largest angle = 144° The measure of the smallest angle = 36° Hence, the difference = 144° - 36° = 108°

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