Question

Question 108
State whether the statements are True or False.
The interior angles of a triangle are in the ratio 1 : 2 : 3, then the ratio of its exterior angles is 3 : 2 : 1.

Answer 1

False
Given, the ratio of interior angles = 1 : 2 : 3.
Let the interior angles be x, 2x and 3x.
So, $x+2x+3x={180}^{\circ }$ [angle sum property of triangle]
$\Rightarrow 6x={180}^{\circ }\Rightarrow x=\frac{{180}^{\circ }}{6}={30}^{\circ }$
$\therefore$ The interior angles are ${30}^{\circ },{60}^{\circ }$ and ${90}^{\circ }$.
Now, the exterior angles will be $({180}^{\circ }-{30}^{\circ }),({180}^{\circ }-{60}^{\circ })$ and $({180}^{\circ }-{90}^{\circ })$
i.e. ${150}^{\circ },{120}^{\circ }$ and ${90}^{\circ }$.
The ratio of exterior angles $={150}^{\circ }:{120}^{\circ }:{90}^{\circ }=15:12:9=5:4:3$.