Question

One of the angles of a triangle is $60°$. The other two angles are in the ratio $2:3$. The measure of the smallest angle is$\_\_\_\_\_\_$

Answer 1

Given

One of the angles of a triangle$=60°$

Other two angles in the ratio $2:3$

Let the other two angles be $2xand3x$

$\because$The sum of all angles in a triangle is $180°$

$$\begin{gathered} \Rightarrow 60+2x+3x=180 \\ \Rightarrow 60+5x=180 \\ \Rightarrow 5x=180-60 \\ \Rightarrow 5x=120 \\ \Rightarrow x=\frac{120}{5} \\ \Rightarrow x=24° \end{gathered}$$

So, the angles are

$$\begin{gathered} 2x=2\times 24=48° \\ 3x=3\times 24=72° \end{gathered}$$

$\therefore$ the measure of the angles are $48°,60°and72°$

Hence, the measure of the smallest angle is $48°$