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Q.32

Expert-verified
Found in: Page 541

### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776

# The ratio of the angle measures of a triangle is $1:2:3$. Classify the triangle by its angle measures.Acute G. Obtuse H. Right I. Equiangular

The triangle will be right. Option H is correct.

See the 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:

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

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

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

## Step 4. Conclusion.

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