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2 Which type of angle creates an arc whose measure is congruent to the angle's measure? A Angle formed by two secants B Angle formed by two tangents c) Inscribed angle D) Central angle

2 Which type of angle creates an arc whose measure is congruent to the angle's measure? A Angle formed by two secants B Angle formed by two tangents c) Inscribed angle D) Central angle

Elementary Geometry For College Students, 7e
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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**Question 2/25** Which type of angle creates an arc whose measure is congruent to the angle’s measure? A) Angle formed by two secants B) Angle formed by two tangents C) Inscribed angle D) Central angle --- **Explanation:** The question asks about the type of angle that creates an arc where the arc's measure is equal to the measure of the angle itself. - **Central Angle (D)**: This is the correct answer. A central angle is one whose vertex is at the center of the circle. The measure of the arc it intercepts is equal to the measure of the angle. - **Angle formed by two secants (A)**: This type of angle is not directly related to arc measures being congruent. - **Angle formed by two tangents (B)**: This angle does not create an arc with a measure congruent to the angle. - **Inscribed Angle (C)**: An inscribed angle intercepts an arc that is twice its measure, so it does not satisfy the condition in the question. This question enhances understanding of the relationships between angles and arcs in circle geometry.
Transcribed Image Text:**Question 2/25** Which type of angle creates an arc whose measure is congruent to the angle’s measure? A) Angle formed by two secants B) Angle formed by two tangents C) Inscribed angle D) Central angle --- **Explanation:** The question asks about the type of angle that creates an arc where the arc's measure is equal to the measure of the angle itself. - **Central Angle (D)**: This is the correct answer. A central angle is one whose vertex is at the center of the circle. The measure of the arc it intercepts is equal to the measure of the angle. - **Angle formed by two secants (A)**: This type of angle is not directly related to arc measures being congruent. - **Angle formed by two tangents (B)**: This angle does not create an arc with a measure congruent to the angle. - **Inscribed Angle (C)**: An inscribed angle intercepts an arc that is twice its measure, so it does not satisfy the condition in the question. This question enhances understanding of the relationships between angles and arcs in circle geometry.
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