Question

If the angles in a triangle are in the ratio 1 : 3 : 5, then the smallest and largest angles are

• A. ${20}^{\circ },{100}^{\circ }$
• B. ${60}^{\circ },{100}^{\circ }$
• C. ${60}^{\circ },{80}^{\circ }$
• D. ${20}^{\circ },{60}^{\circ }$

Answer 1

The correct option is A ${20}^{\circ },{100}^{\circ }$

Let the angles be $x^{\circ },3x^{\circ }$ and $5x^{\circ }$

$\Rightarrow x+3x+5x={180}^{\circ }$

$\Rightarrow 9x={180}^{\circ }$

$\Rightarrow x=\frac{{180}^{\circ }}{9}={20}^{\circ }$

Smallest angle, $x={20}^{\circ }$
Largest angle, $5x=5\times {20}^{\circ }={100}^{\circ }$