Inscribed Angle Theorem

Inscribed Angle Theorem

Learning Targets

• I can investigate the relationship between central angles and inscribed angle in a circle.

• I can understand and apply the Inscribed Angle Theorem in solving real-life problems.

Investigate:

Directions: Access the link and observe the illustration of the inscribed angle and central angle. Then, answer the following questions that follow.


Link: https://www.geogebra.org/m/eh5vcb8g

Multiple Choice

Based on the activity, what can you infer about the relationship between the central angle and the inscribed angle in a circle?

• The central angle is twice the measure of the inscribed angle.

• The central angle and the inscribed angle are always equal.

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

• The central angle and the inscribed angle have no fixed relationship.

Multiple Choice

If the measure of the central angle is 150 degrees, what is the measure of the inscribed angle?

• 50 degrees

• 150 degrees

• 75 degrees

• 100 degrees

Multiple Choice

If the measure of the central angle is given by the expression 3x−2 and the inscribed angle is x+5,

what are the corresponding measures if x=12?

• Central angle = 30 degrees, Inscribed angle = 15 degrees

• Central angle = 40 degrees, Inscribed angle = 20 degrees

• Central angle = 50 degrees, Inscribed angle = 25 degrees

• Central angle = 34 degrees, Inscribed angle = 17 degrees

Open Ended

With your observation above focusing on the Inscribed angle, state the Inscribed Angle Theorem in your own words.