Question

The ratio of the angle measures of a triangle is $1:2:3$. Classify the triangle by its angle measures.

1. Acute G. Obtuse H. Right I. Equiangular

Short answer

The triangle will be right. Option H is correct.

Step-by-step solution

Step 1. Given Information.

Ratio of angle measures of a triangle is $1:2:3$.

Step 2. Concept Used.

Angle sum property of triangle.

$\angle A+\angle B+\angle C=180°$

Step 3. Calculation.

According to angle sum property of triangle,

$\angle A+\angle B+\angle C=180°$

Let angles be x,2x,and 3x respectively.

Substitute the value of$\angle A$, $\angle B$and$\angle C$.

$\begin{array}{c}x+2x+3x=180\\ 6x=180\\ x=\frac{180}{6}\\ x=30\end{array}$

Angles are:

$\begin{array}{c}1x=1\times 30\\ =30°\end{array}$

$\begin{array}{c}2x=2\times 30\\ =60°\end{array}$

$\begin{array}{c}3x=3\times 30\\ =90°\end{array}$

Step 4. Conclusion.

Since, one angle is$90°$, it is a right-angled triangle. Thus, option H is the correct option.