Chapter 6.4, Problem 4CYU

To determine

The measure of angle TSR.

Answer to Problem 4CYU

  $m\angle TSR=56.5$

Explanation of Solution

Given:

The given diagram is:

  $ST=3\frac{13}{16}\text{ feet, PS = 7 feet and m}\angle \text{PTQ = 67}$

Calculation:

As the vertical angles are congruent, thus, $\angle STR\cong \angle PTQ.$

So,

  $\begin{array}{l}m\angle STR=m\angle PTQ\\ m\angle STR=67\end{array}$

In a parallelogram that is also a rectangle, the diagonals are congruent and bisect one another.

Therefore, triangle TSR is an isosceles triangle.

According to Isosceles Triangle Theorem, $\angle TSR\cong \angle TRS.$

The sum of the interior angles of a triangle is 180 degrees.

  $\begin{array}{l}m\angle TSR+m\angle TRS+m\angle STR=180\\ m\angle TSR+m\angle TSR+67=180\\ 2\left(m\angle TSR\right)=113\\ m\angle TSR=56.5\end{array}$