Question

What is the sum of all the exterior angles of a triangle?

• A. ${360}^{\circ }$
• B. ${180}^{\circ }$
• C. ${540}^{\circ }$
• D. ${100}^{\circ }$

Answer 1

The correct option is A

${360}^{\circ }$

$\text{By the exterior angle property,}\angle ACD=\angle BAC+\angle ABC...\left(i\right)\angle BAE=\angle ABC+\angle ACB...\left(ii\right)\angle CBF=\angle ACB+\angle BAC...\left(iii\right)$

$\therefore \text{Sum of exterior angles of}△ABC$
$=\angle ACD+\angle BAE+\angle CBF$ $=2(\angle ABC+\angle ACB+\angle BAC)$

$\text{We know that,}\angle ABC+\angle BAC+\angle ACB={180}^{\circ }\text{(Angle sum property)}$

$\therefore \text{Sum of exterior angles}=2\times \left({180}^{\circ }\right)={360}^{\circ }$