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Question

The average of 3 angles of a quadrilateral which are in the ratio of 2:4:5 is 77o. Find all the angles of the quadrilateral.

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Solution

Let 2x,4x and 5x be the 3 angles of given quadrilateral and m be the fourth angle of the same quadrilateral.

Therefore,

2x+4x+5x3=77

11x=231

x=23111=21

Therefore,

2x=2×21=42

4x=4×21=84

5x=5×21=105

The three angles of the quadrilateral are 42o,84o and 105o.

Therefore,

As we know that sum of internal angles of a quadrilateral is 360o.

42+84+105+m=360

m=360231=129o

Hence the angles of the given quadrilateral are 42o,84o,105o and 129o.
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