Chapter 6.4, Problem 3CYU

To determine

The measure of angle TQR.

Answer to Problem 3CYU

  $m\angle TQR=33.5$

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:

If a parallelogram is a rectangle, the diagonals bisect each other and are congruent.

Therefore, triangle TQR is an isosceles triangle.

According to Isosceles Triangle Theorem;

  $\angle TQR\cong \angle TRQ.$

According to Exterior Angle Theorem, the measure of the exterior angle in a triangle is equal to the sum of measure of 2 remote interior angles.

  $\begin{array}{l}m\angle TQR+m\angle TRQ=m\angle PTQ\\ m\angle TQR+m\angle TQR=67\\ 2\left(m\angle TQR\right)=67\\ m\angle TQR=33.5\end{array}$