Geometry - Angles in Circles

Front

What is the measure of arc AB if it is given as 142 degrees?

Back

Arc AB measures 142 degrees.

Front

What is an angle in a circle with its vertex on the circle itself?

Back

An inscribed angle.

Front

If an inscribed angle intercepts an arc of 24 degrees, what is the measure of the angle?

Back

The inscribed angle measures 12 degrees.

Front

How do you determine the measure of an arc in a circle?

Back

To find the measure of an arc, you can use the central angle that intercepts the arc.

Front

What is a cyclic quadrilateral?

Back

A cyclic quadrilateral is a four-sided figure where all vertices lie on the circumference of a circle.

Front

In a cyclic quadrilateral, the opposite angles are supplementary. What does this mean?

Back

It means that the sum of the measures of each pair of opposite angles equals 180 degrees.

Front

If angle X in a cyclic quadrilateral measures 106 degrees and angle Y measures 93 degrees, what is the measure of angle Z?

Back

Angle Z measures 74 degrees.

Front

What is the relationship between the inscribed angle and the arc it intercepts?

Back

The inscribed angle is half the measure of the intercepted arc.

Front

What is a central angle in a circle?

Back

A central angle is an angle whose vertex is at the center of the circle and whose sides intersect the circle.

Front

If the measure of arc PE is 50 degrees, what is the measure of arc PG if arc PG is supplementary to arc PE?

Back

Arc PG measures 130 degrees.