Chapter 12, Problem 7CR

To determine

To find: The value of the angle $m\angle V$ .

Answer to Problem 7CR

Thevalue of the angle is $m\angle V=16°$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Observe from the given diagram that,

  $\begin{array}{c}m\angle S=74°\end{array}$

     $\begin{array}{c}=m\angle T\end{array}$

Also,

  $\begin{array}{c}m\angle U=90°\end{array}$

     $\begin{array}{c}=m\angle R\end{array}$

Then, by the third angle theorem,

  $m\angle V=m\angle Q$

Then, by angle sum property,

  $\begin{array}{l}m\angle T+m\angle U+m\angle V=180°\\ 74°+90°+m\angle V=180°\\ m\angle V=16°\end{array}$