Chapter 11.2, Problem 13IP

To determine

To find: Measures of the angles.

Answer to Problem 13IP

Angles are ${12}^0,{72}^0,{96}^0$

Explanation of Solution

Given information:

Measures of the angles of a triangle are in the ratio $1:6:8$

Given

Measures of the angles of a triangle are in the ratio $1:6:8$

Let measures of the given angles of a triangle be $x,6x$ and $8x$

We know sum of angles of a triangle is ${180}^0$

Using that

We get

  $x+6x+8x={180}^0$

On solving

  $\begin{array}{l}x+6x+8x={180}^0\\ \Rightarrow 15x={180}^0\\ \Rightarrow x=\frac{{180}^0}{15}\\ \Rightarrow x^0={12}^0\end{array}$

Therefore,

  $x={12}^0$

So, angles are

One of the angles is $x={12}^0$

Second angle is $6x=6\left({12}^0\right)={72}^0$

Third angle is $8x=8\left({12}^0\right)={96}^0$

Therefore,

Angles are ${12}^0,{72}^0,{96}^0$