Here are the answers to the questions provided in the image along with brief explanations:

1. What is an angle whose vertex is on a circle and whose sides contain chords of the circle?

   • Answer: B. Inscribed angle
   • Explanation: An inscribed angle is formed when the vertex lies on the circle, and its sides are chords of the circle.

2. An arc of a circle measures 30°. If the radius of the circle is 1.5 cm, what is the length of the arc?

   • Answer: B. 2.3 cm
   • Explanation: The formula for the arc length is $(\theta / 360) \cdot 2\pi r$. Substituting, $(30/360) \cdot 2 \cdot \pi \cdot 1.5 \approx 2.3 \, \text{cm}$.

3. Using the figure below, which of the following is an external secant segment of $\overline{OM}$?

   • Answer: C. $\overline{OM}$
   • Explanation: An external secant segment is the part of the secant line that lies outside the circle.

4. The opposite angles of a quadrilateral inscribed in a circle are _____.

   • Answer: D. Supplementary
   • Explanation: In a cyclic quadrilateral (a quadrilateral inscribed in a circle), opposite angles add up to 180°.

5. In $\odot S$ at the right, what is $m \angle VSI$ if $m \angle VI = 140°$?

   • Answer: A. 35°
   • Explanation: $m \angle VSI$ is half the measure of the intercepted arc, so $140° / 2 = 35°$.

6. What is the sum of the measures of the central angles of a circle with no common interior points?

   • Answer: C. 360°
   • Explanation: The sum of all central angles in a circle always equals 360°.

Let me know if you need detailed step-by-step explanations for any of these questions or further clarification.

Related Questions:

1. How is the measure of an inscribed angle related to the arc it intercepts?
2. How can you calculate the arc length of a sector if the radius and angle are given?
3. What are the key properties of cyclic quadrilaterals?
4. How do central angles differ from inscribed angles in a circle?
5. What is the relationship between external secant segments and tangents?

Tip:

Always remember to identify whether the angle is central, inscribed, or external, as their relationships with arcs