Question

The sum of the exterior angles of a triangle is $m^0$. Find $m$

Answer 1

Sum of interior angles of a triangle=${180}^{\circ }$

$⟹\alpha +\beta +\gamma ={180}^{\circ }$ -(1)

sum of angles on a straight line=${180}^{\circ }$

$⟹$ Exterior angles:

$\angle A={180}^{\circ }-\alpha$

$\angle B={180}^{\circ }-\beta$

$\angle C={180}^{\circ }-\gamma$

sum of exterior angles:

$⟹$(180x3)-$(\alpha +\beta +\gamma )$

$⟹$540-(180) -from(1)

$⟹$ 540-180=360

$\therefore$ $m$=${360}^{\circ }$