Chapter 9.2, Problem 44STP

To determine

To find: The largest angle measured.

Answer to Problem 44STP

The largest angle measured is $105°$ .

Explanation of Solution

Given:

The smallest angle of a triangle is two thirds of the measure of middle angle.

The middle angle is three sevenths of the measure of the largest angle.

Calculation:

Let $A$ be the smallest angle, $B$ be the middle angle and $C$ be the largest angle.

From the given information,

  $\begin{array}{c}A=\frac{2}{3}B\\ B=\frac{3}{7}C\end{array}$

In a triangle $A+B+C=180°$ .

Convert angle $A$ in terms of $C$ .

  $\begin{array}{c}A=\frac{2}{3}B\\ =\frac{2}{3}\left(\frac{3}{7}C\right)\\ =\frac{2}{7}C\end{array}$

Add all the angles.

  $\begin{array}{c}\frac{2}{7}C+\frac{3}{7}C+C=180\\ \frac{2+3+7}{7}C=180\\ C=\frac{7}{12}\left(180\right)\\ =105°\end{array}$

Therefore, the largest angle measured is $105°$ .