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Determine the measure of the angle or arc in the following figures. Write your answer on the space provided. Figure for items 1-3. Point Q is the center of the circle. 1. If the measure of minor AB is 75°, find the measure of the following: a. MZBQC b. MBAC Q C 2. If mBAC = 297°, find the measure of the following: %3D a. mBC b. m 2 BỌC 3. If ZBOC = 82° determine the measure of the following: a. MZQBC b. m 2QCB %3D C. m CAB

Determine the measure of the angle or arc in the following figures. Write your answer on the space provided. Figure for items 1-3. Point Q is the center of the circle. 1. If the measure of minor AB is 75°, find the measure of the following: a. MZBQC b. MBAC Q C 2. If mBAC = 297°, find the measure of the following: %3D a. mBC b. m 2 BỌC 3. If ZBOC = 82° determine the measure of the following: a. MZQBC b. m 2QCB %3D C. m CAB

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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Name: Grade & Section: Date: Score: Competency 22 (M10GE-lic-1): Derives inductively the relations among chords, arcs, central angles, and inscribed angles. Worksheet 22.2 FINDING THE MEASURES OF THE ARCS, CENTRAL AND INSCRIBED ANGLES OF A CIRCLE Key Points A centrai angle is an angle whose vertex is the center of the circle. ZAOBis a central arngle. The minor arc AB is the union of points A and B and all the points of the circle in the interior of ZAOB. The major arc ACB is the union of points A and B and all points of the circle in the exterior of ZAOB. The semicircle is all points of the circle that lie on one side of the diameter. eunion of the endpoints of a diameter and Arc Measures of a Circle: The degree measure of the minor arc is equal to the degree measure of the central angle. The degree measure of the major arc is equal to 360 minus the degree measure of the related minor arc The degree measure of the semicircie is 1830. One complete circle measures 360 degrees. in the same circle or in congruent circles, arcs which have the same measure are congruent arcs. An Inscribed angle is an angle whose vertex lies on the circle and whose sides contain chords of the circle, like ZBAC. The measure of an inscribed angie is equal to one-half the measure of its intercepted arc; mZBAC = Determine the measure of the angle or arc in the following figures. Write your answer on the space provided. Figure for items 1-3. Point Q is the center of the circle. 1. If the measure of minor AB is 75°, find the measure of the following: a. MZBQC b. MBAC 2. If mBAC = 297°, find the measure of the following: a. mBC b. m 2 BỌC 3. If m ZBOC = 82° determine the measure of the following: a. MZQBC b. m 2QCB C. m CAB 41
Transcribed Image Text:Name: Grade & Section: Date: Score: Competency 22 (M10GE-lic-1): Derives inductively the relations among chords, arcs, central angles, and inscribed angles. Worksheet 22.2 FINDING THE MEASURES OF THE ARCS, CENTRAL AND INSCRIBED ANGLES OF A CIRCLE Key Points A centrai angle is an angle whose vertex is the center of the circle. ZAOBis a central arngle. The minor arc AB is the union of points A and B and all the points of the circle in the interior of ZAOB. The major arc ACB is the union of points A and B and all points of the circle in the exterior of ZAOB. The semicircle is all points of the circle that lie on one side of the diameter. eunion of the endpoints of a diameter and Arc Measures of a Circle: The degree measure of the minor arc is equal to the degree measure of the central angle. The degree measure of the major arc is equal to 360 minus the degree measure of the related minor arc The degree measure of the semicircie is 1830. One complete circle measures 360 degrees. in the same circle or in congruent circles, arcs which have the same measure are congruent arcs. An Inscribed angle is an angle whose vertex lies on the circle and whose sides contain chords of the circle, like ZBAC. The measure of an inscribed angie is equal to one-half the measure of its intercepted arc; mZBAC = Determine the measure of the angle or arc in the following figures. Write your answer on the space provided. Figure for items 1-3. Point Q is the center of the circle. 1. If the measure of minor AB is 75°, find the measure of the following: a. MZBQC b. MBAC 2. If mBAC = 297°, find the measure of the following: a. mBC b. m 2 BỌC 3. If m ZBOC = 82° determine the measure of the following: a. MZQBC b. m 2QCB C. m CAB 41
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