Chapter 8.7, Problem 59SPR

To determine

To calculate:

The value of $m\angle 6$ in a quadrilateral $WXYZ$

Answer to Problem 59SPR

The value of $m\angle 6$ is $60$ in a quadrilateral $WXYZ$ .

Explanation of Solution

Given information:

  

  $m\angle 1=30$

Calculation:

  

From Figure, know that the opposite sides of the rectangle are always parallel.

  $\overline{WX}=\overline{YZ}$

The theorem of alternate interior angles:

  $\begin{array}{l}m\angle 5=m\angle 1\\ m\angle 5=30\end{array}$

Definition of the rectangle,

  $\angle WYZ$ is right angle.

  $\angle 5$ and $\angle 6$ are complementary angles.

Complementary angles definition shows that:

  $m\angle 6+m\angle 5=90\mathrm{...}\left(1\right)$

Put the value of $m\angle 5=30$ in equation (1):

  $\begin{array}{l}m\angle 6+30=90\\ m\angle 6=60\end{array}$

Hence, the value of $m\angle 6$ is $60$ in a quadrilateral $WXYZ$ .