25. A polygon is tangent to the circle. 26. If a central angle measures 25 , then the measure of its intercepted arc is 27. The part of a circle included between two of its points is a/an 28. If inscribed $$ \angle B $$ measures 48 , then the measure of its intercepted arc, $$ \overparen{A C} $$, is 29. If inscribed $$ \angle C $$ intercepts $$ \overparen{B D} $$, which measures 214 , then the angle measures 30. $$ \angle A $$ is formed by two tangents and measures 36 . The measure of intercepted $$ \overparen{B C} $$ is 144 . What is the measure of $$ \overparen{B D C} $$ ? 31. If central $$ \angle A $$ intercepts $$ \overparen{B C} $$, which measures 113 , then $$ \angle A $$ measures 32. Two chords intersect within a circle and form an angle measuring 65 . The measure of one intercepted arc is 79 . Let $$ \overparen{B C} $$ be the measure of the other arc. What is the measure of $$ \overparen{B C} $$ ? 3.

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UpStudy AI · Accepted Answer

Sure, let's go through each of the questions you've listed from 25 to 32. I'll provide answers and brief explanations for each.

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### **25. A polygon is**
*It seems like this question is incomplete. If you provide the full question, I'd be happy to help!*

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### **26. If a central angle measures 25°, then the measure of its intercepted arc is**
**Answer:** 25°

**Explanation:** 
- The measure of a central angle is equal to the measure of its intercepted arc. 
- **Central Angle = Intercepted Arc**
  
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### **27. The part of a circle included between two of its points is a/an**
**Answer:** Arc

**Explanation:** 
- An **arc** is the part of the circumference of a circle between two points.
  
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### **28. If inscribed $$ \angle B $$ measures 48°, then the measure of its intercepted arc, $$ \overparen{AC} $$, is**
**Answer:** 96°

**Explanation:** 
- The measure of an inscribed angle is half the measure of its intercepted arc.
- **Intercepted Arc = 2 × Inscribed Angle**
- $$ \overparen{AC} = 2 × 48° = 96° $$

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### **29. If inscribed $$ \angle C $$ intercepts $$ \overparen{BD} $$, which measures 214°, then the angle measures**
**Answer:** 107°

**Explanation:** 
- As with the previous question, the inscribed angle is half the measure of its intercepted arc.
- $$ \angle C = \frac{214°}{2} = 107° $$

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### **30. $$ \angle A $$ is formed by two tangents and measures 36°. The measure of intercepted $$ \overparen{BC} $$ is 144°. What is the measure of $$ \overparen{BDC} $$?**
**Answer:** 216°

**Explanation:** 
- When two tangents intersect outside a circle, the angle between them is half the difference of the measures of the intercepted arcs.
- Given:
  - $$ \angle A = 36° $$
  - $$ \overparen{BC} = 144° $$
- Let the other intercepted arc be $$ \overparen{BDC} = x° $$
- Formula: $$ \angle A = \frac{|x - 144°|}{2} $$
- $$ 36° = \frac{|x - 144°|}{2} $$
- $$ |x - 144°| = 72° $$
- Since the total degrees in a circle is 360°, $$ x = 144° + 72° = 216° $$

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### **31. If central $$ \angle A $$ intercepts $$ \overparen{BC} $$, which measures 113°, then $$ \angle A $$ measures**
**Answer:** 113°

**Explanation:** 
- A central angle is equal in measure to its intercepted arc.
- **Central Angle = Intercepted Arc**
- $$ \angle A = 113° $$

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### **32. Two chords intersect within a circle and form an angle measuring 65°. The measure of one intercepted arc is 79°. Let $$ \overparen{BC} $$ be the measure of the other arc. What is the measure of $$ \overparen{BC} $$?**
**Answer:** 51°

**Explanation:** 
- When two chords intersect inside a circle, the measure of the angle formed is half the sum of the measures of the intercepted arcs.
- Formula: $$ 	ext{Angle} = \frac{	ext{Arc}_1 + 	ext{Arc}_2}{2} $$
- Given:
  - $$ 	ext{Angle} = 65° $$
  - $$ 	ext{Arc}_1 = 79° $$
- Let $$ 	ext{Arc}_2 = x° $$
- $$ 65° = \frac{79° + x°}{2} $$
- $$ 130° = 79° + x° $$
- $$ x° = 130° - 79° = 51° $$

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If you have any more questions or need further clarification on any of these topics, feel free to ask!
**25. A polygon is** *Incomplete question. Please provide the full question for a complete answer.* --- **26. If a central angle measures 25°, then the measure of its intercepted arc is** 25° --- **27. The part of a circle included between two of its points is a/an** Arc --- **28. If inscribed $$ \angle B $$ measures 48°, then the measure of its intercepted arc, $$ \overparen{AC} $$, is** 96° --- **29. If inscribed $$ \angle C $$ intercepts $$ \overparen{BD} $$, which measures 214°, then the angle measures** 107° --- **30. $$ \angle A $$ is formed by two tangents and measures 36°. The measure of intercepted $$ \overparen{BC} $$ is 144°. What is the measure of $$ \overparen{BDC} $$?** 216° --- **31. If central $$ \angle A $$ intercepts $$ \overparen{BC} $$, which measures 113°, then $$ \angle A $$ measures** 113° --- **32. Two chords intersect within a circle and form an angle measuring 65°. The measure of one intercepted arc is 79°. Let $$ \overparen{BC} $$ be the measure of the other arc. What is the measure of $$ \overparen{BC} $$?** 51°

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