Finding Missing Angle Measurements in Circles using the Intersecting Chord Theorem

This lesson covers finding missing angle measurements within a circle using the intersecting chord theorem. It reviews the central and exterior angle theorems, explains the difference between arc measure and arc length, and applies the intersecting chord theorem to solve for angle relationships. An example problem is provided to demonstrate the application of these concepts.

What does the central angle theorem state about the inscribed angle?

• It is half the measure of the intercepted arc.

• It is twice the measure of the intercepted arc.

• It is equal to the intercepted arc.

• It is unrelated to the intercepted arc.

How does the exterior angle theorem relate to a triangle?

• The exterior angle is equal to the adjacent interior angle.

• The exterior angle is the sum of the remote interior angles.

• The exterior angle is half the sum of the interior angles.

• The exterior angle is unrelated to the interior angles.

What is the difference between arc measure and arc length?

• Arc measure is the angle, while arc length is the distance.

• Arc measure is the distance, while arc length is the angle.

• Arc measure is always greater than arc length.

• Both are the same and interchangeable.

According to the intersecting chord theorem, what is the measure of angle AEC?

• It is half the sum of the measures of arcs BD and AC.

• It is equal to the measure of arc AC.

• It is equal to the measure of arc BD.

• It is twice the sum of the measures of arcs BD and AC.

If the measure of arc BD is 100 degrees and arc AC is 150 degrees, what is the measure of angle AEC?

• 150 degrees

• 175 degrees

• 125 degrees

• 100 degrees