Chapter 4.2, Problem 3CCYP

To determine

To find: The measure of the angle $\mathrm{m}\angle 4$ .

Answer to Problem 3CCYP

The measure of angle is $38°$ .

Explanation of Solution

Given Data:

The given diagram shown in Figure 1

  

Figure 1

Calculation:

Consider the angle sum property that sum of all the angles in a triangle is 180 degree.

Since the triangle is right angle triangle so one of the angle is of 90 degrees.

Then,

  $\begin{array}{l}90°+\mathrm{m}\angle 3+38°=180°\\ \mathrm{m}\angle 3=52°\end{array}$

Thus, the measure of angle is $52°$ .

Consider the angle 3 is,

  $90°-52°=38°$

Then,

  $\begin{array}{l}90°+\mathrm{m}\angle 4+52°=180°\\ \mathrm{m}\angle 4=180-142°\\ \mathrm{m}\angle 4=38°\end{array}$