Question

The ratio of the angle of a triangle is$2:3:7$. Find the angle measures. Then classify the triangle by its angle measures.

Short answer

The angles measures are $30{}^{\circ },45{}^{\circ },105°$ respectively.

The triangle is a scalene triangle.

Step-by-step solution

Step 1. Given Information.

The ratio of angle of a triangle is$2:3:7$.

Step 2. Concept Used.

Angle sum property of triangle.

$\angle A+\angle B+\angle C=180°$

Step 3. Calculation.

Let the angle measures be 2x, 3x, 7x.

The sum of all the angles of a triangle is 180. Hence,

$2x+3x+7x=180°$

Adding all the x on the left side of the equation.

$12x=180°$

Divide both the sides by 12.

$\frac{12x}{12}=\frac{180}{12}$

This will give the value of$x=15$.

Hence the angle measures are:

First angle is 2x, multiply 2 with 15.

$\begin{array}{l}2x=2\times 15\\ =30\end{array}$

Second angle 3x, multiply 3 with 15.

$\begin{array}{l}3x=3\times 15\\ =45\end{array}$

Third angle is 7x, multiply 7 with 15.

$\begin{array}{l}7x=7\times 15\\ =105\end{array}$

As all the angle measures are different, which implies that all the sides of the triangle are of different lengths. Hence the triangle is scalene triangle.

Step 4. Conclusion.

The angle measures of the triangle are $30{}^{\circ },45{}^{\circ },105°$ and the triangle can be classified as scalene triangle.