Inscribed Angle Theorem

Free interactive math game: Inscribed Angle Theorem — Central = 2·inscribed. Part of the Geometry (Angles) category on MathKite.

Example problems

Taken from the generator that powers this exercise. A fresh set appears every time the page is opened, and the printable worksheet holds ten of them.

  1. The central angle of a circle is 80°. Find the inscribed angle subtending the same arc.
  2. The central angle of a circle is 50°. Find the inscribed angle subtending the same arc.
  3. An inscribed angle in a circle is 60°. Find the central angle subtending the same arc.
  4. An inscribed angle in a circle is 50°. Find the central angle subtending the same arc.

About this exercise

Angles drawn inside a circle from its edge.

How to solve it

An inscribed angle is half the central angle standing on the same arc. An angle in a semicircle is always 90 degrees.

Worked example

A central angle of 80 degrees gives an inscribed angle of 40.

Common mistake

Doubling instead of halving. The central angle is the larger of the two.