Question

The angles of a quadrilateral are in the ratio 1:2:2:5.Find the difference between the measures of the largest and the smallest angle.

Answer 1

Hey there!

Let the angles of the quadrilateral be x, 2x, 2x, & 5x......

In a quadrilateral, sum of interior angles is 360 - by angle sum property of quadrilateral.

This way,

x + 2x + 2x + 5x = 360

10x = 360

x = 360 ÷ 10

x = 36 degree..........
2x = 2×36 = 72 degree......
2x = 2×36 = 72 degree......
5x = 5×36 = 180 degree........


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Answer 2

let the angle be 1x 2x 2x 5x

1x +2x +2x +5x =360
10x = 360
x = 360 ÷10
x =36

1x =1×36
x = 36
2x =2×36
x = 72
2x =2×36
x = 72
5x =5×36
x =180

largest angle- smaller angle
180-36
144 ans