Question

If all the sides of a triangle are produced in order to form exterior angles , prove that the sum of the exterior angles so formed is 360 degree

Answer 1

In a triangle, let the angles be x, y and z


We know that the interior angles sum up to form 180°, that is the sum of interior angles of a triangle is 180°

» x + y + z = 180°

Now the exterior angles would be 180 - x, 180 - y, 180 - z as the exterior angle and interior angle form linear pair.

So we have to find the sum of exterior angle

=> 180 - x + 180 - y + 180 - z

= 540 - x - y - z

= 540 - (x + y + z)

= 540 - 180

= 360°

Hence, the sum of exterior angle of a triangle = 360°



Another way,


We know that exterior angle = sum of two opposite angles.

So exterior angle 1 = x + y
second = y + z
third = x + z

So their sum = x + y + y + z + x + z

= 2x + 2y + 2z

= 2( x + y + z)

= 2(180)

= 360°

Hence proved

Answer 2

Answer:

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