Chapter 8.1, Problem 2CE

To determine

To find: the angles $m\angle RSU$ , $m\angle TSU$ and $m\angle T$ .

Answer to Problem 2CE

The angles $m\angle RSU$ , $m\angle TSU$ and $m\angle T$ are $90-k$ , $k$ and $90-k$ .

Explanation of Solution

Given:

The right triangles are shown below:

Angle $m\angle R$ is k.

Calculation:

Angle $m\angle RSU$ is calculated as follows:

  $\begin{array}{l}m\angle RSU+m\angle RUS+m\angle R=180\left(\text{Sum}\text{of}\text{angles}\text{of}\text{}\text{triangle}\right)\\ m\angle RSU+90+k=180\\ m\angle RSU=180-90-k\\ m\angle RSU=90-k\end{array}$

Angle $m\angle TSU$ is calculated as follows:

  $\begin{array}{l}m\angle RSU+m\angle TSU=90\left(\text{Right }\text{}\text{triangle}\Delta TRS\right)\\ 90-k+m\angle TSU=90\\ m\angle TSU=k\end{array}$

Angle $m\angle T$ is calculated as follows:

  $\begin{array}{l}m\angle RST+m\angle R+m\angle T=180\left(\text{Sum}\text{of}\text{angles}\text{of}\text{}\text{triangle}\right)\\ 90+k+m\angle T=180\\ m\angle T=180-90-k\\ m\angle T=90-k\end{array}$

Thus, the angles $m\angle RSU$ , $m\angle TSU$ and $m\angle T$ are $90-k$ , $k$ and $90-k$ .