Question

The three angles of a triangle are in the ratio $1:2:3$. The measure of the smallest angle is$\_\_\_\_\_\_$

Answer 1

Given the three angles of a triangle in ratio $1:2:3$

Let the measure of three angles of a triangle be $x,2xand3x$

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

$$\begin{gathered} \Rightarrow x+2x+3x=180 \\ \Rightarrow 6x=180 \\ \Rightarrow x=\frac{180}{6} \\ \Rightarrow x=30° \end{gathered}$$

So, the three angles of the triangle are

$$\begin{gathered} x=30° \\ 2x=2\times 30=60° \\ 3x=3\times 30=90° \end{gathered}$$

Hence, the measure of the smallest angle is $30°$.