Secants, Tangents, and Angles Answers

1

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Which formula would be used to find the measure of angle 1?

A

(a° + b°).

B

(a° – c°).

C

(b° + c°).

D

(a° – b°).

2

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

A

When two tangents intersect outside a circle, the angle formed has a measure that is one half the difference of the intercepted arcs.

B

The measures of the intercepted arcs are both 180 degrees.

C

One half times (180 – 180) = 0.

116544

What are the measures of angles 1 and 2?

Answers:

m∠1 = °:50

m∠2 = °:130

116545

47100✔ 130 133

A

47

B

100

C

✔ 130

D

133

116547

What are the measures of angles 1 and 2?

Answers:

Angles JHI and GJH are inscribed angles. We have that m∠JHI = b and m∠GJH = a by the . Angle JHI is an exterior angle of triangle . Because the measure of an exterior angle is equal to the sum of the:GJH

Angles JHI and GJH are inscribed angles. We have that m∠JHI = b and m∠GJH = a by the . Angle JHI is an exterior angle of triangle . Because the measure of an exterior angle is equal to the sum of the:substitution property

116548

BEAFJI✔ GJHJIH

A

BEA

B

FJI

C

✔ GJH

D

JIH

116549

reflexive property✔ substitution propertysymmetric propertytransitive property

A

reflexive property

B

✔ substitution property

C

symmetric property

D

transitive property

116556

⇒ 250

Answer:

116556

116557

What is the measure of angle ABC?

A

42.5°

B

67.5°

C

85°

D

135°

116558

⇒ 58

Answer:

116546

116559

What is the measure of angle AOC?

A

42°

B

58°

C

66°

D

79°

116560

⇒ 194

Answer:

116555

116561

A satellite views the Earth at an angle of 20°. What is the arc measure, x, that the satellite can see?

A

40°

B

80°

C

160°

D

320°

116562

Two tangents each intersect a circle at opposite endpoints of the same diameter. Is it possible for the two tangents to intersect each other outside the circle? Explain why or why not, using the information you learned in this lesson.

Answer:

No, it is not possible for the two tangents to intersect. By definition, a tangent is perpendicular to the radius at the point of tangency. Since the tangents are at opposite endpoints of the same diameter, they are both perpendicular to the same line (the diameter). Therefore, the two tangent lines are parallel and will never intersect. Alternatively, the measure of the angle formed by two tangents is half the difference of the intercepted arcs. If the endpoints are a diameter, both arcs are 180 degrees, and half of (180 - 180) is 0, meaning no angle or intersection is formed.

116563

central angles theorem✔ inscribed angle theoremangle formed by secants or tangents theoremangle formed by two chords theorem

Answers:

Angles JHI and GJH are inscribed angles. We have that m∠JHI = b and m∠GJH = a by the . Angle JHI is an exterior angle of triangle . Because the measure of an exterior angle is equal to the sum of the:inscribed angle theorem

Angles JHI and GJH are inscribed angles. We have that m∠JHI = b and m∠GJH = a by the . Angle JHI is an exterior angle of triangle . Because the measure of an exterior angle is equal to the sum of the:GJH

Angles JHI and GJH are inscribed angles. We have that m∠JHI = b and m∠GJH = a by the . Angle JHI is an exterior angle of triangle . Because the measure of an exterior angle is equal to the sum of the:substitution property

Secants, Tangents, and Angles Answers

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