The Inscribed Angle Theorem states that in a circle, an angle inscribed in the arc (formed by two chords sharing a common endpoint on the circumference) is exactly half the measure of the central angle that subtends the same arc. For instance, if a central angle measures 100 degrees, the inscribed angle subtending the same arc will measure 50 degrees. This theorem is essential for understanding relationships between angles and arcs in circle geometry, aiding in the calculation of unknown angles in various geometric figures.
Table of Contents
- Part 1: OnlineExamMaker AI Quiz Maker – Make A Free Quiz in Minutes
- Part 2: 20 Inscribed Angle Theorem Quiz Questions & Answers
- Part 3: AI Question Generator – Automatically Create Questions for Your Next Assessment
Part 1: OnlineExamMaker AI Quiz Maker – Make A Free Quiz in Minutes
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Part 2: 20 Inscribed Angle Theorem Quiz Questions & Answers
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1. Question: In a circle, an inscribed angle subtends an arc of 80 degrees. What is the measure of the inscribed angle?
A) 40 degrees
B) 80 degrees
C) 160 degrees
D) 40 radians
Correct Answer: A) 40 degrees
Explanation: The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of the arc it subtends. So, half of 80 degrees is 40 degrees.
2. Question: If a central angle in a circle measures 120 degrees, what is the measure of an inscribed angle that subtends the same arc?
A) 60 degrees
B) 120 degrees
C) 240 degrees
D) 30 degrees
Correct Answer: A) 60 degrees
Explanation: According to the Inscribed Angle Theorem, an inscribed angle is half the central angle that subtends the same arc, so half of 120 degrees is 60 degrees.
3. Question: An inscribed angle in a circle subtends a semicircle. What is the measure of the inscribed angle?
A) 90 degrees
B) 180 degrees
C) 45 degrees
D) 360 degrees
Correct Answer: A) 90 degrees
Explanation: A semicircle has an arc measure of 180 degrees, and the inscribed angle is half of that, which is 90 degrees.
4. Question: If an inscribed angle measures 35 degrees, what is the measure of the arc it subtends?
A) 70 degrees
B) 35 degrees
C) 17.5 degrees
D) 140 degrees
Correct Answer: A) 70 degrees
Explanation: The Inscribed Angle Theorem indicates that the arc measure is twice the inscribed angle, so twice 35 degrees is 70 degrees.
5. Question: In a circle, two inscribed angles subtend the same arc. If one angle is 50 degrees, what is the measure of the other?
A) 50 degrees
B) 100 degrees
C) 25 degrees
D) 200 degrees
Correct Answer: A) 50 degrees
Explanation: Inscribed angles that subtend the same arc are equal, so both angles measure 50 degrees.
6. Question: An inscribed angle subtends an arc of 150 degrees. What is the measure of the inscribed angle?
A) 75 degrees
B) 150 degrees
C) 300 degrees
D) 75 radians
Correct Answer: A) 75 degrees
Explanation: The theorem states that the inscribed angle is half the arc it subtends, so half of 150 degrees is 75 degrees.
7. Question: If the central angle is 90 degrees, what is the inscribed angle subtending the same arc?
A) 45 degrees
B) 90 degrees
C) 180 degrees
D) 22.5 degrees
Correct Answer: A) 45 degrees
Explanation: The inscribed angle is half the central angle for the same arc, so half of 90 degrees is 45 degrees.
8. Question: An inscribed angle measures 20 degrees. What is the central angle for the same arc?
A) 40 degrees
B) 20 degrees
C) 10 degrees
D) 80 degrees
Correct Answer: A) 40 degrees
Explanation: The central angle is twice the inscribed angle for the same arc, so twice 20 degrees is 40 degrees.
9. Question: In a circle, an inscribed angle subtends an arc of 360 degrees. What is the measure of the inscribed angle?
A) 180 degrees
B) 360 degrees
C) 90 degrees
D) 720 degrees
Correct Answer: A) 180 degrees
Explanation: An arc of 360 degrees is the full circle, and the inscribed angle subtending it is half, which is 180 degrees (a straight angle).
10. Question: If an inscribed angle is 60 degrees, what is the measure of the arc it subtends?
A) 120 degrees
B) 60 degrees
C) 30 degrees
D) 240 degrees
Correct Answer: A) 120 degrees
Explanation: The arc measure is twice the inscribed angle, so twice 60 degrees is 120 degrees.
11. Question: A circle has an inscribed angle of 72 degrees. What is the central angle for the same arc?
A) 144 degrees
B) 72 degrees
C) 36 degrees
D) 288 degrees
Correct Answer: A) 144 degrees
Explanation: The central angle is twice the inscribed angle for the same arc, so twice 72 degrees is 144 degrees.
12. Question: An inscribed angle subtends a 100-degree arc. What is the measure of the angle?
A) 50 degrees
B) 100 degrees
C) 200 degrees
D) 25 degrees
Correct Answer: A) 50 degrees
Explanation: The inscribed angle is half the arc measure, so half of 100 degrees is 50 degrees.
13. Question: If two inscribed angles subtend arcs of 40 degrees each, what are their measures?
A) 20 degrees each
B) 40 degrees each
C) 80 degrees each
D) 10 degrees each
Correct Answer: A) 20 degrees each
Explanation: Each inscribed angle is half the arc it subtends, so each is half of 40 degrees, which is 20 degrees.
14. Question: An inscribed angle measures 85 degrees. What is the arc measure?
A) 170 degrees
B) 85 degrees
C) 42.5 degrees
D) 340 degrees
Correct Answer: A) 170 degrees
Explanation: The arc is twice the inscribed angle, so twice 85 degrees is 170 degrees.
15. Question: In a circle, the central angle is 200 degrees. What is the inscribed angle for the same arc?
A) 100 degrees
B) 200 degrees
C) 400 degrees
D) 50 degrees
Correct Answer: A) 100 degrees
Explanation: The inscribed angle is half the central angle, so half of 200 degrees is 100 degrees.
16. Question: An inscribed angle subtends a 60-degree arc. What is its measure?
A) 30 degrees
B) 60 degrees
C) 120 degrees
D) 15 degrees
Correct Answer: A) 30 degrees
Explanation: The inscribed angle is half the arc, so half of 60 degrees is 30 degrees.
17. Question: If an inscribed angle is 15 degrees, what is the central angle for the same arc?
A) 30 degrees
B) 15 degrees
C) 7.5 degrees
D) 60 degrees
Correct Answer: A) 30 degrees
Explanation: The central angle is twice the inscribed angle, so twice 15 degrees is 30 degrees.
18. Question: An inscribed angle subtends an arc of 270 degrees. What is the angle’s measure?
A) 135 degrees
B) 270 degrees
C) 540 degrees
D) 67.5 degrees
Correct Answer: A) 135 degrees
Explanation: The inscribed angle is half the arc, so half of 270 degrees is 135 degrees.
19. Question: Two inscribed angles subtend the same 90-degree arc. What is each angle’s measure?
A) 45 degrees
B) 90 degrees
C) 180 degrees
D) 22.5 degrees
Correct Answer: A) 45 degrees
Explanation: Inscribed angles subtending the same arc are equal and each is half the arc, so half of 90 degrees is 45 degrees.
20. Question: If the inscribed angle is 40 degrees, what is the measure of the arc it subtends?
A) 80 degrees
B) 40 degrees
C) 20 degrees
D) 160 degrees
Correct Answer: A) 80 degrees
Explanation: The arc measure is twice the inscribed angle, so twice 40 degrees is 80 degrees.
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Part 3: AI Question Generator – Automatically Create Questions for Your Next Assessment
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