Chapter 12.1, Problem 20E

To determine

To find: the measurement of acute angles.

Answer to Problem 20E

The acute angles are ${22}^0,{68}^0$ .

Explanation of Solution

Given:

  

Concept used:

If the triangle is right triangle then sum of the other two angles is ${90}^0$ .

Sum of the three angles of triangle is always ${180}^0$ .

If the triangle is right triangle then other two angles other than ${90}^0$ will be less than ${90}^0$ .

Calculation:

If the triangle is right triangle then sum of the other two angles is ${90}^0$ .

  $\begin{array}{l}{\left(3x+2\right)}^0+x^0={90}^0.\\ 4x+2=90.\\ 4x=88.\\ x=22.\end{array}$

So, the two acute angles are:

  $\begin{array}{l}x={22}^0.\\ 3x+2=3\left(22\right)+2={68}^0.\end{array}$

Hence, the acuteanglesare ${22}^0,{68}^0$ .