Q. 1235.0( 3 Votes )

If the sides of a triangle are produced in an order, show that the sum of the exterior angles so formed is 360°.

Answer :

Formula Used/Theory:-

Angle sum property

Sum of all angles of triangle is 180°

Exterior angle is equal to sum of interior opposite angles

Let 3 angle of triangle be x;y;z

Exterior angle opposite of x will be y + z

Exterior angle opposite of y will be x + z

Exterior angle opposite of z will be x + y

sum of all 3 exterior angles will be

(y + z) + (x + z) + (x + y)

= 2x + 2y + 2z

= 2(x + y + z)

By angle sum property of triangle

x + y + z = 180°

sum of exterior angles is 2(x + y + z)

= 2× 180° = 360°

Result:- sum of exterior angles is 360°

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