Question

Use the diagram to complete each statement.

If $m\angle R=k,$ then $m\angle RSU=?,$

$m\angle TSU=?,$ and $m\angle T=?.$

Short answer

The final answer is $m\angle RSU$, \$[m\angle TSU\mathrm{\backslash ]}$ and $m\angle T$ are .$90-k$, $k$ and $90-k$.

Step-by-step solution

Step 1. Given information:

The right angles are shown below.

$m\angle R=k$

Step 2. Concept used.

In a triangle the sum of angles is $180°$.

Step 3. applying the concept.

Now, we write the angles and their sum.

In triangle RSU,

$\begin{array}{l}m\angle RSU+m\angle RUS+m\angle R=180\left(\text{Sum\hspace{0.33em}of\hspace{0.33em}angles\hspace{0.33em}oftriangle}\right)\\ m\angle RSU+90+k=180\\ m\angle RSU=180-90-k\\ m\angle RSU=90-k\end{array}$

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

$\begin{array}{l}m\angle RSU+m\angle TSU=90\left(\text{Righttriangle\hspace{0.33em}}\Delta TRS\right)\\ 90-k+m\angle TSU=90\\ m\angle TSU=k\end{array}$

Angle $m\angle T$is as follows:

$\begin{array}{l}m\angle RST+m\angle R+m\angle T=180\left(\text{Sum\hspace{0.33em}of\hspace{0.33em}angles\hspace{0.33em}oftriangle}\right)\\ 90+k+m\angle T=180\\ m\angle T=180-90-k\\ m\angle T=90-k\end{array}$

Therefore, the complete given statement is $m\angle RSU$,$m\angle TSU$and $m\angle T$are $90-k$, k and $90-k.$