Finding the Measure of Circumscribed Angles: Relationships with Central Angles

This lesson explores the relationships between central and circumscribed angles within quadrilaterals. It defines central and circumscribed angles, provides examples, and demonstrates how to calculate angle measures using derived formulas. The lesson also covers the properties of quadrilaterals, specifically kites, and their angle relationships. An example problem is solved to illustrate the application of these concepts.

What is a central angle?

• An angle whose vertex is outside the circle and rays are tangent to the circle.

• An angle formed by two intersecting chords.

• An angle that measures exactly 90 degrees.

• An angle whose vertex is at the center of the circle and sides intersect the circle.

Which of the following is true about a circumscribed angle?

• It is formed by two intersecting chords.

• Its vertex is at the center of the circle.

• Its rays are tangent to the circle.

• It is always equal to the central angle.

In a quadrilateral with two right angles, what is the sum of the measures of the central and circumscribed angles?

• 270 degrees

• 180 degrees

• 360 degrees

• 90 degrees

If the central angle measures 60 degrees, what is the measure of the circumscribed angle?

• 90 degrees

• 120 degrees

• 60 degrees

• 180 degrees

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

• The central angle is double the measure of the arc.

• The central angle is half the measure of the arc.

• The central angle is equal to the measure of the arc.

• The central angle is unrelated to the arc measure.