Question

Find the sum of all the exterior angles of a triangle.

• A. 60°
• B. 90°
• C. 360°
• D. 180°

Answer 1

The correct option is C

360°

In the above figure shown, 1, 2 and 3 are the interior angles whereas 4, 5 and 6 are exterior angles. Using linear pair axiom, we can say that:
1 + 4 = ${180}^{\circ }$
3 + 6 = ${180}^{\circ }$
2 + 5 = ${180}^{\circ }$
Adding all of them, we get:
(1 + 4) + (3 + 6) + (2 + 5) = ${540}^{\circ }$
Rearranging the terms, we get:
(1 + 2 + 3) + (4 + 5 + 6) = ${540}^{\circ }$
1 + 2 + 3 = ${180}^{\circ }$ (Angle Sum Property of a triangle)
So, (4 + 5 + 6) = ${540}^{\circ }$ - ${180}^{\circ }$ = ${360}^{\circ }$
So, the sum of the exterior angles of a triangle is ${360}^{\circ }$.