Question

m∠vwu = ______
m∠uwt = ______
m∠twx = ______
true or false (overrightarrow{wu}) and (overrightarrow{wx}) are opposite rays.

Explanation:

Step1: Find $m\angle VWU$

The angle next to $\angle VWU$ is $130^{\circ}$, and they are supplementary (sum to $180^{\circ}$). So $m\angle VWU=180 - 130=40^{\circ}$.

Step2: Find $m\angle UWT$

There is a right - angle symbol at $\angle UWT$, so $m\angle UWT = 90^{\circ}$.

Step3: Find $m\angle TWX$

$\angle TWX$ and the $130^{\circ}$ angle are vertical angles. Vertical angles are equal, so $m\angle TWX = 130^{\circ}$.

Step4: Determine if $\overrightarrow{WU}$ and $\overrightarrow{WX}$ are opposite rays

Opposite rays are two rays that have the same endpoint and form a straight line. $\overrightarrow{WU}$ and $\overrightarrow{WX}$ do not form a straight line, so the statement is False.

Answer:

1. $m\angle VWU = 40^{\circ}$
2. $m\angle UWT = 90^{\circ}$
3. $m\angle TWX = 130^{\circ}$
4. False