Question

The angles of a triangle are in the ratio $3:4:5.$ Find the smallest angle.

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${75}^o$

Answer 1

The correct option is B ${45}^o$

Given that the angles of a triangle are in the ratio $3:4:5.$

Let the measure of the angles be $3x,4x,5x.$

We know that, the sum of the angles of a triangle $={180}^{\circ }$

So,

$3x+4x+5x={180}^{\circ }$

$\Rightarrow 12x={180}^{\circ }$

$\Rightarrow x=\frac{{180}^{\circ }}{12}$

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

Therefore,

Smallest angle $=3x$

$=3\times {15}^{\circ }$

$={45}^{\circ }$