Question

The measures of angles of a triangle are in the ratio $1:2:3$. Determine the measures of smallest angle of the triangle.

Answer 1

Let the angles be $A=x,B=2x,C=3x$

$\Rightarrow x+2x+3x={180}^o$

$\Rightarrow 6x={180}^o$

$\Rightarrow x={30}^o$

Therefore, $A=1\times {30}^o={30}^o$,

$B=2\times {30}^o={60}^o$

and $C=3\times {30}^o={90}^o$

Therefore, the smallest angle is ${30}^o$.