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

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.

Question 3

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

Revolt · Accepted Answer

✔ substitution property

Question 4

The measure of ∠B is (3x – 4 )° and the measure of ∠D is (2x – 6)°. What are the measures of angles B and D?

Revolt · Accepted Answer

✔ 110; m∠B = °: 110; m∠D = °: 70

Question 5

35 38✔ 7076

Revolt · Accepted Answer

✔ 70

Question 6

Given: ∠KJL and ∠KML intercept arc KL.

Revolt · Accepted Answer

♦ =: inscribed angle thm.; ♠ =: substitution property

Question 7

What are the measures of and ∠KIJ?

Revolt · Accepted Answer

⇒ 104: 115654; 52

Question 8

Question 115655

Revolt · Accepted Answer

52

Inscribed Angles Answers

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