Central Angles

Question 1

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 2

♠ =

Revolt · Accepted Answer

substitution property

Question 3

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

Revolt · Accepted Answer

100°

Question 4

What are the measures of and ∠KIJ? Measure of = ° Measure of ∠KIJ = °

Revolt · Accepted Answer

Part 1: 104; Part 2: 52

Question 5

The measure of arc QS is (4x – 18)°.What is the value of x?

Revolt · Accepted Answer

49.5

Question 6

∠FAE measures 72°. What other angle must measure 72°?

Revolt · Accepted Answer

∠FBE

Question 7

38 76✔ 110 210

Revolt · Accepted Answer

110; Selection 1: 110; Selection 2: 70

Question 8

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 9

What is the measure of ?

Revolt · Accepted Answer

50°

Question 10

angle formed by a tangent and a chord thm.✔ inscribed angle thm. second corollary to the inscribed angle thm. substitution property

Revolt · Accepted Answer

inscribed angle thm.

Central Angles Answers

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