Chapter 6.1, Problem 10WE

To determine

To prove: $\angle VXZ$is an obtuse angle.

Answer to Problem 10WE

Explanation of Solution

Given information: Given $\overline{VY}\perp \overline{YZ}$

  

Calculation:

Given $\overline{VY}\perp \overline{YZ}$

  $\begin{array}{c}\angle XYZ={90}^{\circ }=\angle Y\\ \angle Y+\angle Z+\angle YXZ={180}^{\circ }(△\text{}\text{property})\\ \angle Z+\angle YXZ={180}^{\circ }-\angle Y\\ \angle Z+\angle YXZ={180}^{\circ }-{90}^{\circ }={90}^{\circ }\\ \text{So}\angle YXZ<{90}^{\circ }\text{because}\angle Z>0\\ \text{Since}\angle YXZ+\angle VXZ={180}^{\circ }\\ \text{since}\angle YXZ<{90}^{\circ }\\ So{180}^{\circ }>\angle VXZ>{90}^{\circ }\end{array}$

Therefore , $\angle VXZ$ is an obtuse angle.

Hence proved.