91Ó°ÊÓ

The ratio of angles of a triangle is$6:5:4$.

Let the angle measures be 6x, 5x, 4x.

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

$6x+5x+4x=180°$

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

$15x=180°$

Divide both the sides by 15.

$\frac{15x}{15}=\frac{180°}{15}$

This will give the value of$x=12$.

Hence the angle measures are:

First angle is 6x, multiply 6 with 12.

$\begin{array}{l}6x=6×12\\ =72\end{array}$

Second angle 5x, multiply 5 with 12.

$\begin{array}{l}5x=5×12\\ =60\end{array}$

Third angle is 4x, multiply 4 with 12.

$\begin{array}{l}4x=4×12\\ =48\end{array}$

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.

The angle measures of the triangle are $72{}^{∘},60{}^{∘},48°$ and the triangle can be classified as scalene triangle.