Question

The angles of a triangle are in the ratio of $1:2:3$.

Find the measure of each angle of the triangle. What type of triangle is it?

Answer 1

Given : Ratio of angles of triangle $=1:2:3$

Let common ratio be '$\mathrm{x}$'

So, angles of triangle are $\mathrm{x},2\mathrm{x},3\mathrm{x}$

We know that sum of angles of triangle is $180°$.

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

And $2\mathrm{x}=2\times 30$

$=60°$

And $3\mathrm{x}=3\times 30$

$=90°$

Since one of the angles is $90°$, so it is a Right angled triangle.

Hence, the measurement of angles of the triangle are ${90}^{\mathrm{o}},{60}^{\mathrm{o}},{30}^{\mathrm{o}}$ and it is a right angle triangle.