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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