Inscribed Angles and Arcs — Practice Geometry Questions

In geometry, when you have an inscribed angle on a circle, the measure of the inscribed angle and the length of the intercepted arc are related.

An inscribed angle is equal to half of the intercepted arc.

The following practice questions ask you to find the measure of an inscribed arc and an inscribed angle.

Practice questions

1. Equilateral triangle

   

   is inscribed in Circle O.

   

   Find the missing arc

   

2. In Circle O,

   

   is a right triangle with diameter

   

   as the hypotenuse.

   

   If

   

   and OR = 20, find

   

Answers and explanations

1. 120 degrees

   

   is equilateral, which means all sides of the triangle are equal. This also means that

   

2. 60 degrees

   The inscribed angle of a circle is half the measure of the intercepted arc: