Chapter 5.6, Problem 4CYU

To determine

To find:Thegreater angle between $m\angle XWZ$ and $m\angle YZW$ .

Answer to Problem 4CYU

The angle $m\angle XWZ>m\angle YZW$ .

Explanation of Solution

Given Information:

The given figure is

  

Formula Used:

Hinge theorem is

If two sides of a triangle correspond to two sides of another triangle, and the angle of inclination of the first triangle is greater than the angle of inclination of the second triangle, so the sides of the first triangle are longer than the sides of the third side of the second triangle.

From the figure, $\overline{YZ}\cong \overline{XW}$ . Segment $YZ$ measures $7$ and segment $XW$ measures $7$ , so they have equal measures and rare therefore congruent.

Again $\overline{WZ}\cong \overline{WZ}$ , reflexive property of congruent

  $WY<ZX$ , Segment $WY$ measures $2.1$ and segment $ZX$ measures $2.3$ .

  $m\angle XWZ>m\angle YZW$ . Thus by converse of the Hinge theorem, $\angle YZW$ is less than $\angle XWZ$ , so $\angle XWZ$ is greater than $\angle YZW$ .

Hence, the angle $m\angle XWZ>m\angle YZW$ .