12. In cirde O, m z ABOC=62". Find m AC A C 620

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
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Find m
**Question:**

In circle O, m∠ABC = 62°. Find m∠AC (inscribed angle subtended by arc AC).

**Diagram:**

A diagram of a circle with center O is provided. The circle has three points on its circumference: A, B, and C, where:

- ∠ABC = 62° as marked in the diagram.
- There are lines connecting A to B, B to C, and A to C forming a triangle within the circle.
- The angle at point B is 62°.

**Answer Options:**
- A. 248°
- B. 236°
- C. 62°
- D. 124°

**Details:**

To find the angle measure for m∠AC, remember that the inscribed angle theorem states that the inscribed angle is half the measure of the intercepted arc. Since m∠ABC is given as 62°, then the intercepted arc AC must be twice that.

Given that the central angle subtended by arc AC is twice the inscribed angle:

Central angle subtended by arc AC = 2 * 62° = 124°

Thus, the correct answer is:

- D. 124°
Transcribed Image Text:**Question:** In circle O, m∠ABC = 62°. Find m∠AC (inscribed angle subtended by arc AC). **Diagram:** A diagram of a circle with center O is provided. The circle has three points on its circumference: A, B, and C, where: - ∠ABC = 62° as marked in the diagram. - There are lines connecting A to B, B to C, and A to C forming a triangle within the circle. - The angle at point B is 62°. **Answer Options:** - A. 248° - B. 236° - C. 62° - D. 124° **Details:** To find the angle measure for m∠AC, remember that the inscribed angle theorem states that the inscribed angle is half the measure of the intercepted arc. Since m∠ABC is given as 62°, then the intercepted arc AC must be twice that. Given that the central angle subtended by arc AC is twice the inscribed angle: Central angle subtended by arc AC = 2 * 62° = 124° Thus, the correct answer is: - D. 124°
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