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
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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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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