Chapter 15.3, Problem 17PSB

To determine

To Arrange: The angles of the given figure in descending order.

Answer to Problem 17PSB

  $\angle XZW>\angle X>\angle XWY>\angle Y>\angle XWZ$

Explanation of Solution

Given:

  $\begin{array}{l}WX=13\\ WY=15\\ XZ=5\\ ZY=9\end{array}$

  

Formula Used:

The Hinge Theorem: It states that if two sides of two triangles are congruent and angle of one is greater than the angle of second then the third side of the triangle will be greater than the another.

Angle opposite to larger side in triangle is always larger and vice-versa.

Calculation:

  $\begin{array}{l}WX=13\\ WY=15\\ XZ=5\\ ZY=9\\ XY=XZ+ZY=5+9=14\end{array}$

  $\begin{array}{l}\text{Angel opposite to }WXis\angle WYXor\angle Y\&\angle XZW\\ \text{Angel opposite to }WYis\angle WXYor\angle X\&\angle WZY\\ \text{Angel opposite to }XZis\angle XWZ\\ \text{Angel opposite to }ZYis\angle ZWY\\ \text{Angel opposite to }XYis\angle XWY\end{array}$

  $\angle XZW>\angle X>\angle XWY>\angle Y>\angle XWZ$

Conclusion:

Thus the arranged order of the angles are shown in the calculation section