Chapter 7.1, Problem 5PSA

To determine

To calculate: Measure of each angle of triangle

Answer to Problem 5PSA

Measure of angles are $48°$ , $60°$ and $72°$ .

Explanation of Solution

Given information : Here, we have given that the angles of triangle are in the ratio $4:5:6$

Formula used : Sum of all angles of triangle is $180°$

Calculation: Let the common measure between all the angles be $x°$ .

  $\therefore$ The angles will be $4x$ , $5x$ and $6x$ .

As, sum of all angles of triangle is $180°$ .

  $\begin{array}{l}\Rightarrow 4x+5x+6x=180°\\ \Rightarrow 15x=180°\\ \Rightarrow x=\frac{180°}{15}\\ \Rightarrow x=12°\end{array}$

Now, putting $x=12°$ in $4x$ , $5x$ and $6x$ , we get

  $\begin{array}{l}\Rightarrow 4x=4(12°)=48°\\ \Rightarrow 5x=5(12°)=60°\\ \Rightarrow 6x=6(12°)=72°\end{array}$

  $\therefore$ Angles are $48°$ , $60°$ and $72°$ .