Question

If the sides of a triangle are produced, then the sum of the exterior angle i.e. $\angle a+\angle b+\angle c$ is equal to:

• A. ${180}^0$
• B. ${360}^0$
• C. ${90}^0$
• D. ${270}^0$

Answer 1

The correct option is B ${360}^0$

In $△ABC$,
$\angle a=\angle ABC+\angle ACB$ (Exterior angle property)
$\angle b=\angle ACB+\angle BAC$ (Exterior angle property)
$\angle C=\angle ABC+\angle BAC$ (Exterior angle property)
Adding all the equations:
$\angle a+\angle b+\angle c=2(\angle ABC+\angle ACB+\angle BAC)$
$\angle a+\angle b+\angle c=2\left({180}^o\right)$
$\angle a+\angle b+\angle c={360}^{\circ }$.

Therefore, option $B$ is correct.