Question

The side of the triangle are produced in order. The sum of the three exterior Angel so formed is

Answer 1

The side of the triangle are produced in order. The sum of the three exterior Angel so formed is equal to four right angles


In triangle ABC

Let exterior angles be X,Y,Z

So,

angle X= angle ( A + B) .. (1)

angle Y = angle (B+C) ..(2)

angle Z = angle (A+C) ..(3)

On adding X,Y,and Z

angle (X+Y+Z) = 2(angle A + angle B+angleC)

angle (X+Y+Z) = 2 x 180 (By angle sum property of triangle)

angle (X+Y+Z) = 2 x (2 x 90)

Thus we get that sum of the exterior angles of a triangle is equal to four right angles