Angles and Arcs in Circles

What is a central angle?

• An angle with its vertex at the center of the circle

• An angle with its vertex inside of the circle

• An angle with its vertex on the circumference of the circle

• An angle with its vertex on the outside of the circle

What is an inscribed angle?

• An angle with its vertex at the center of the circle

• An angle with its vertex inside of the circle

• An angle with its vertex on the circumference of the circle

• An angle with its vertex on the outside of the circle

What is an angle in the interior of a circle?

• An angle with its vertex at the center of the circle

• An angle with its vertex inside of the circle

• An angle with its vertex on the circumference of the circle

• An angle with its vertex on the outside of the circle

What is an angle in the exterior of a circle?

• An angle with its vertex at the center of the circle

• An angle with its vertex inside of the circle

• An angle with its vertex on the circumference of the circle

• An angle with its vertex on the outside of the circle

The measurement of an angle in the interior is

• The same as the measurement of the arc it makes on the circle

• Half of the measurement of the arc it makes on the circle

• Half of the sum of the measurements of the two arcs it makes on the circle

• Half of the difference of the measurements of the two arcs it makes on the circle

The measurement of an inscribed angle is

• The same as the measurement of the arc it makes on the circle

• Half of the measurement of the arc it makes on the circle

• Half of the sum of the measurements of the two arcs it makes on the circle

• Half of the difference of the measurements of the two arcs it makes on the circle

The measurement of a central angle is

• The same as the measurement of the arc it makes on the circle

• Half of the measurement of the arc it makes on the circle

• Half of the sum of the measurements of the two arcs it makes on the circle

• Half of the difference of the measurements of the two arcs it makes on the circle

The measurement of an angle in the exterior is

• The same as the measurement of the arc it makes on the circle

• Half of the measurement of the arc it makes on the circle

• Half of the sum of the measurements of the two arcs it makes on the circle

• Half of the difference of the measurements of the two arcs it makes on the circle

An inscribed quadrilateral is a quadrilateral

• that is located somewhere inside of a circle

• with at least one vertex on the circumference of a circle

• with all four vertices on the circumference of a circle

• that crosses through a circle

What is special about an inscribed quadrilateral?

• Both pairs of opposite angles are congruent

• Both pairs of opposite sides are congruent

• Both pairs of opposite angles are supplementary

• Duh, both pairs of opposite sides are supplementary!