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.

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. --- ### **25. A polygon is** *It seems like this question is incomplete. If you provide the full question, I'd be happy to help!* --- ### **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** --- ### **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. --- ### **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** - \( \overparen{AC} = 2 × 48° = 96° \) --- ### **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. - \( \angle C = \frac{214°}{2} = 107° \) --- ### **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°, \( x = 144° + 72° = 216° \) --- ### **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** - \( \angle A = 113° \) --- ### **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: \( \text{Angle} = \frac{\text{Arc}_1 + \text{Arc}_2}{2} \) - Given: - \( \text{Angle} = 65° \) - \( \text{Arc}_1 = 79° \) - Let \( \text{Arc}_2 = x° \) - \( 65° = \frac{79° + x°}{2} \) - \( 130° = 79° + x° \) - \( x° = 130° - 79° = 51° \) --- If you have any more questions or need further clarification on any of these topics, feel free to ask!