Question

An exterior angle of a triangle is ${80}^{\circ }$ and the interior opposite angles are in the ratio 1 : 3. Measure of each interior opposite angle is :

• A. ${30}^{\circ },{90}^{\circ }$
• B. ${40}^{\circ },{120}^{\circ }$
• C. ${20}^{\circ },{60}^{\circ }$
• D. ${30}^{\circ },{60}^{\circ }$

Answer 1

The correct option is C ${20}^{\circ },{60}^{\circ }$

Let the interior angles be $x$ and $3x$

We know that exterior angle of triangle is equal to sum of interior opposite angles.

$\Rightarrow x+3x={80}^{\circ }\Rightarrow 4x={80}^{\circ }\Rightarrow x={20}^{\circ }$

So the angles are

$x={20}^{\circ }3x=3\times {20}^{\circ }={60}^{\circ }$

So option $C$ is correct.