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Question

In a quadrilateral the angles are in the ratio 2:4:5:7 then find the difference between the greatest and the smallest angle.

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Solution

Sum of a angle of a quadrilateral =360°
The ratio of angles =2:4:5:7
let the angles be 2x,4x,5x,7x.
So, 2x+4x+5x+7x=360°18x=360°x=20°

So, 1st angle =2x=40°
2nd angle =4x=80°
3rd angle =5x=100°
4th angle =7x=140°
Hence, difference between the greatest and smallest angle = 140o40o=100o

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