Chapter 15.3, Problem 8PSB

(a)

To determine

To Prove: In the given figure angle XWZ is greater than angle WZY

Explanation of Solution

Given:

  $\begin{array}{l}\to ▱WXYZ\\ \to XZ>WY\end{array}$

Concept Used:

Properties of rectangle: Opposite sides of rectangle are congruent.

Properties of triangle: Sum of interior angle of a triangle is equal to 180.

Calculation:

  

Statements	Cause
$▱WXYZ$	$\text{Given}$
$XZ>WY$	$\text{Given}$
$WX=YZ\text{ and XY=WZ}$	$\text{Rectangle definition}$
$XYZ\text{ and }YZW\text{ triangles}$	$XYZ\text{ and }YZW\text{ has two same sides, }XZ\text{ and }WY\text{ is different}$
$\angle XWZ>\angle WZY$	$\text{Since }XZ>WY$

Conclusion:

Thus from the given condition it is proved that $\angle XWZ>\angle WZY$

(b)

To determine

To Prove: In the given figure angle XWZ is obtuse

Explanation of Solution

Given:

  $\begin{array}{l}\to ▱WXYZ\\ \to XZ>WY\end{array}$

Concept Used:

Properties of rectangle: Opposite sides of rectangle are congruent.

Properties of triangle: Sum of interior angle of a triangle is equal to 180.

Calculation:

  

  $\begin{array}{l}\to WXYZ\text{ is rectangle}\\ \to \angle XWZ+\angle WZY={180}^o\\ \to \angle XWZ>\angle WZY\left(\text{proved in part a}\right)\\ \text{⇒}\angle XWZ\text{ is obtuse}\end{array}$

Conclusion:

Thus the $\angle XWZ$ is obtuse