Let's solve the problems in the image.

Problem 5

In the circle, the arc $\overset{\frown}{BC}$ is labeled $80^\circ$. We need to find the measure of arc $\overset{\frown}{BA}$.

• The total measure of a circle is $360^\circ$.
• The measure of the remaining arc $\overset{\frown}{BA}$ can be calculated by subtracting $\overset{\frown}{BC}$ from $360^\circ$: $\overset{\frown}{BA} = 360^\circ - 80^\circ = 280^\circ$

Answer for Problem 5: The measure of $\overset{\frown}{BA}$ is $280^\circ$.

Problem 6

In the circle, the central angle $\angle XWV$ is $42^\circ$. We need to find the measure of arc $\overset{\frown}{WV}$.

• In a circle, the measure of an arc is equal to the measure of its corresponding central angle.
• Hence, the measure of arc $\overset{\frown}{WV}$ is: $\overset{\frown}{WV} = 42^\circ$

Answer for Problem 6: The measure of $\overset{\frown}{WV}$ is $42^\circ$.

Let me know if you'd like further clarifications or details! Here are 5 related questions to enhance your understanding:

1. What is the measure of a semicircular arc in a circle?
2. If the measure of an arc is $90^\circ$, what is the measure of its supplementary arc?
3. How can you calculate the measure of an arc using the radius and central angle?
4. If a circle's central angle is $30^\circ$, what fraction of the circle's circumference does the arc cover?
5. Why is the measure of an arc equal to the measure of its central angle?

Tip: Always visualize the relationship between central angles