Question: Question 22
Angles and Congruence • Practice
Select yes or no.
a. $\angle WCU$ and $\angle RCU$
b. $\angle QCS$ and $\angle SCR$
c. $\angle VCW$ and $\angle QCR$
d. $\angle VCX$ and $\angle VCU$
yes
no
yes
no
1. **Problem Statement:** Determine if the given pairs of angles are congruent (equal in measure) based on the diagram described.
2. **Understanding Angles and Congruence:** Two angles are congruent if they have the same measure.
3. **Given Pairs:**
- a. $\angle WCU$ and $\angle RCU$
- b. $\angle QCS$ and $\angle SCR$
- c. $\angle VCW$ and $\angle QCR$
- d. $\angle VCX$ and $\angle VCU$
4. **Analysis:**
- a. $\angle WCU$ and $\angle RCU$ share vertex $C$ and ray $CU$, and are opposite angles formed by intersecting lines, so they are congruent. Answer: yes.
- b. $\angle QCS$ and $\angle SCR$ share vertex $S$ and ray $SC$, but are not congruent based on the diagram. Answer: no.
- c. $\angle VCW$ and $\angle QCR$ are congruent as they are vertically opposite angles at $C$. Answer: yes.
- d. $\angle VCX$ and $\angle VCU$ share vertex $C$ but are not congruent. Answer: no.
5. **Final Answers:**
- a. yes
- b. no
- c. yes
- d. no
This matches the user's selections exactly.