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Grade 9 / The Inscribed Angle Theorem 1 / 6

Inscribed Angles ① Inscribed Angles and Central Angles

An inscribed angle is half the central angle subtending the same arc.

Definitions

  • Central angle: An angle formed by connecting the endpoints of an arc to the center of the circle
  • Inscribed angle: An angle formed by connecting the endpoints of an arc to a point on the circumference
📘 Example ①
If the central angle subtending arc AB is 80°, find the inscribed angle.
Answer: Inscribed angle = central angle ÷ 2 = 80° ÷ 2 = 40°
📘 Example ②
If an inscribed angle subtending the same arc is 35°, find the central angle.
Answer: Central angle = 35° × 2 = 70°
💡 Key Point
  • Inscribed angle = central angle ÷ 2
  • All inscribed angles subtending the same arc are equal.
  • Inscribed angle subtending a semicircular arc = 90°

Practice Problems

  1. If the central angle subtending arc AB is 120°, find the inscribed angle.
  2. If the inscribed angle subtending arc AB is 55°, find the central angle.

Answer and Explanation

  1. Answer: 60°. 120 ÷ 2 = 60.
  2. Answer: 110°. 55 × 2 = 110.
Next
Inscribed Angles ② Proof of the Inscribed Angle Theorem

Questions and answers for this lesson

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