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Question

The sides of a quadrilateral are produced in order. What is the sum of the four exterior angles?


Solution

Let ABCD be a quadrilateral such that exterior angles formed by extending the sides AD,AB,BC and CD are angles x,y,z and w.
Now, since, sides AD,AB,BC and CD are straight lines, therefore,
BAD+x=180BAD=180x...(i) [Linear Pair].
Similarly,
ABC=180y ...(ii)
BCD=180z ...(iii) 
ADB=180w ...(iv)
Adding (i), (ii), (iii) and (iv), we get,
BAD+ABC+BCD+ADB=(180x)+(180y)+(180z)+(180w)
360=720(x+y+z+w) [Sum of all the angles of a quadrilateral is 360]
x+y+z+w=360

Thus, the sum of the four exterior angles is 360.

OR

It is well established that regardless of number of exterior angles, the sum of all the exterior angles of a polygon is always 360.


Mathematics
RD Sharma
Standard VIII

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