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Q.32

Expert-verifiedFound in: Page 541

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.

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

**Angle sum property of triangle.**

$\angle A+\angle B+\angle C=180\xb0$

According to angle sum property of triangle,

$\angle A+\angle B+\angle C=180\xb0$

Let angles be *x*,* *2*x*,* *and 3*x* 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:

$\begin{array}{c}1x=1\times 30\\ =30\xb0\end{array}$

$\begin{array}{c}2x=2\times 30\\ =60\xb0\end{array}$

$\begin{array}{c}3x=3\times 30\\ =90\xb0\end{array}$

Since, one angle is$90\xb0$, it is a right-angled triangle. Thus, option H is the correct option.

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