Chapter 4.2, Problem 39PPS

To determine

The measure of each angle.

Answer to Problem 39PPS

The measure of larger acute angle is 67 and the measure of smaller acute angle is 23.

Explanation of Solution

Given:

The measure of larger acute angle in right triangle is 2 degrees less than three times the measure of the smaller acute angle.

Calculation:

Let the measure of larger acute angle be m and the measure of smaller acute angle be n.

Therefore,

  $\begin{array}{l}m+n=90\\ 3n-2+n=90\\ 4n-2=90\\ 4n=92\\ n=\frac{92}{4}\\ n=23\end{array}$

Now, the value of m will be:

  $\begin{array}{l}m=3n-2\\ m=3\left(23\right)-2\\ m=67\end{array}$

The measure of larger acute angle is 67 and the measure of smaller acute angle is 23.