Inscribed Angles

Question 1

Explain how you can use the inscribed angle theorem to justify its second corollary, that an angle inscribed in a semicircle is a right angle.

Revolt · Accepted Answer

A circle measures 360°, so a semicircle (which is half the circle) measures 180°. According to the inscribed angle theorem, the measure of an inscribed angle is half the measure of its intercepted arc. Since an angle inscribed in a semicircle intercepts an arc of 180°, the measure of the inscribed angle is half of 180°, which is 90°. Therefore, the angle is a right angle.

Question 2

What did you include in your response? Check all that apply.

Revolt · Accepted Answer

A circle measures 360°.; A semicircle measures 180°.; Half of 180° is 90°.; A right angle measures 90°.

Question 3

and are diameters of circle T. What is the measure of ?

Revolt · Accepted Answer

100°

Question 4

What is the measure of ?

Revolt · Accepted Answer

50°

Inscribed Angles Answers

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