​Vertical Angles in a Circle and Arc Measures

About Geometry Worksheet Assignment 10.12:                 

 

Assignment 10.12 is an introduction to the theorem about the measures of vertical angles in a circle and the measures of their intercepted arcs.

 

Prerequisite Skills:  Identify arcs intercepted by lines intersecting a circle (Assignment 10.10).  Solve algebraic equations with one variable.

 

Theorems:  The sum of the measures of a pair of vertical angles in the interior of a circle equals the sum of the measures of the arcs intercepted by the

                           vertical angles.

 

                           The measure of each of a pair of vertical angles in the interior of a circle is one-half the sum of the measures of the arcs intercepted by the

                           angles.