Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Find m

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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