Chapter 8.6, Problem 45E

(a)

To determine

To Find: The measure of $m\angle UWV,m\angle TWU,m\angle TWX.$

Answer to Problem 45E

  $\angle UWV={50}^{°},\angle TWU={40}^{°},\angle TWX={140}^{°}$ .

Explanation of Solution

Given:

  

  $\begin{array}{l}\angle UWV+\angle VWX=180(suplementaryangle)\\ \angle UWV+130=180\\ \angle UWV={50}^{°}\\ \angle TWU+\angle UWV=90(complementary)\\ \angle TWU+50=90\\ \angle TWU={40}^{°}\\ \angle TWX+\angle TWU=180(suplementaryangle)\\ \angle TWX+40=180\\ \angle TWX={140}^{°}\end{array}$

(b)

To determine

To Find: The probability that the angle measure are supplementary.

Answer to Problem 45E

  $\frac{1}{3}$ .

Explanation of Solution

Given:

  

There are total six combinations to pick any two angles out of four and only two of six are supplementary angles.

Thus the probability that the angle measure are supplementary.

  $P=\frac{2}{6}=\frac{1}{3}$