Chapter 7.1, Problem 26WE

To determine

To calculate: The measure of each angle, if the ratio of angles of a triangle is $3:4:5$ .

Answer to Problem 26WE

The measure of the angles of the triangle are $45°,60°and75°$ .

Explanation of Solution

Given information:

The ratio of angles of a triangle is $3:4:5$ .

Formula Used:

Property of triangle:

The sum of all the angles of a triangle is $180°$ .

Calculation:

Let $A,BandC$ are the angles of a triangle.

So, $A+B+C=180°$ .

Consider the ratio of angles of a triangle is $3:4:5$ .

Let the angles be $3x,4xand5x$ .

Now, we find the value of $x$ :

  $\begin{array}{c}3x+4x+5x=180°\\ 12x=180°\\ x=\frac{180°}{12}\\ x=15\end{array}$

Now, we find the angles:

Substitute 15 for $x$ in the angles are $3x,4xand5x$ .

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

  $\begin{array}{c}4x=4\times 15\\ =60\end{array}$

  $\begin{array}{c}5x=5\times 15\\ =75\end{array}$

Hence, the measure of the angles of the triangle are $45°,60°and75°$ .