Question

If the exterior angles of a triangle are in the ratio $4:5:6,$ find the ratio of the angles of the triangle.

Answer 1

Let the angles are $4x,5x$ and $6x$

Sum of exterior angle of a triangle $={360}^{\circ }$

$4x+5x+6x={360}^{\circ }$

$\Rightarrow 15x={360}^{\circ }$

$\Rightarrow x={24}^{\circ }$

First Exterior angle $=4\left(24\right)={96}^{\circ }$

Second Exterior angle $=5\left(24\right)={120}^{\circ }$

third extreior angle $=6\left(24\right)={144}^{\circ }$

Then, First interior angle of the triangle $=180-96={84}^{\circ }$

Second Interior angle of the triangle $=180-120={60}^{\circ }$

Third Interior of the triangle $=180-144={36}^{\circ }$

Ratio of the angles of the triangle $=84:60:36=7:5:3$