Question

One of the exterior angles of a triangle is ${120}^{\circ }$ and the interior opposite angles are in the ratio 1:2. Find the angles of the triangle.

Answer 1

Let the common multiple be x.

$\therefore$ Interior angles are x and 2x

using properly of exterior angle of triangle

Exterior angle = sum of interior opposite angles

$120=x+2x=3x$

$\therefore x={40}^{\circ }$ $\therefore$ Angles are ${40}^{\circ },{60}^{\circ },{80}^{\circ }$

$\therefore$ Angles of triangle are $x=40$

$2x=2\times 40={80}^{\circ }$

third angle $=180-(40+80)={60}^{\circ }$