Chapter 5.4, Problem 17WE

To determine

To find: The angles 2, 3 and 4.

Answer to Problem 17WE

The value of angles 2, 3 and 4 are 32, 58 and 58 respectively.

Explanation of Solution

Given:

The triangle is shown below:

  

The side GM is median of right triangle IRG . Angle 1 is 32.

Calculation:

For the right triangle, median is the half of the hypotenuse.

Hence,

  $RM=MG$

Angles opposite to equal sides in triangle RMG are equal to each other.

  $m\angle 1=m\angle 2=32$

Sum of angles of triangle is 180,

  $\begin{array}{c}m\angle 1+m\angle 2+m\angle 3+m\angle 4=180\\ 32+\left(m\angle 2+m\angle 3\right)+m\angle 4=180\\ 32+90+m\angle 4=180\\ m\angle 4=58\end{array}$

And,

  $\begin{array}{c}m\angle 2+m\angle 3=90\\ 32+m\angle 3=90\\ m\angle 3=58\end{array}$

Thus, the value of angles 2, 3 and 4 are 32, 58 and 58 respectively.