Math 3 Quiz: Circle Angle Relationships
2 questions · exam conditions
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Circle Angle RelationshipsQuestion 1 of 2

In circle R, inscribed angle DEF intercepts arc DF that measures 128°128°. Point G lies on arc DF such that arc DG = 48°48°. What is the measure of angle DEG?

24°24°
40°40°
48°48°
64°64°
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Math 3 Quiz

Math 3 Quiz: Circle Angle Relationships

Practice Circle Angle Relationships in Math 3 with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Circle Angle Relationships, giving you a quick way to practice the rules, question types, and explanations that matter most for Math 3.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

In circle R, inscribed angle DEF intercepts arc DF that measures 128°128°. Point G lies on arc DF such that arc DG = 48°48°. What is the measure of angle DEG?

  1. 24°24° (correct answer)
  2. 40°40°
  3. 48°48°
  4. 64°64°
Explanation: Inscribed angle DEF = 128°/2 = 64°. Since G lies on arc DF with arc DG = 48°, the inscribed angle DEG subtends arc DG. Therefore, angle DEG = 48°/2 = 24°. Choice B would be 80°/2 if arc DG were 80°. Choice C gives the arc measure rather than the inscribed angle. Choice D gives the full angle DEF.

Question 2

In circle V, diameter AB passes through the center. Point C is on the circle such that arc AC = 116°116°. A tangent at point C intersects the extension of diameter AB at point D. What is the measure of angle ACD?

  1. 32°32° (correct answer)
  2. 58°58°
  3. 64°64°
  4. 116°116°
Explanation: Since AB is a diameter, arc AB = 180°. Given arc AC = 116°, then arc CB = 180° - 116° = 64°. The angle between a tangent and a chord equals half the arc cut off by the chord on the side away from the tangent. Since the tangent at C and chord CA form angle ACD, this angle equals half of arc CB (the arc on the opposite side of chord AC from the tangent). Therefore, angle ACD = (arc CB)/2 = 64°/2 = 32°.