Post on 29-Dec-2015
10.4 Inscribed Angles
5/7/2010
Using Inscribed Angles• An inscribed
angle is an angle whose vertex is on a circle and whose sides contain chords of the circle.
• Intercepted arc is an arc that lies in the interior of an inscribed angle and has endpoints on the angle.
intercepted arc
inscribed angle
To find the measure of an arc use the central angle.
Central angle
115˚
115˚
Theorem 10.7: Measure of an Inscribed Angle
• If an angle is inscribed in a circle, then its measure is one half the measure of its intercepted arc.
mADB = ½mAB
A
D
B
130˚
(½)130 = 65˚
Ex. 1: Finding Measures of Arcs and Inscribed Angles
• Find the measure of the blue arc or angle.
Q
RS
T
QTSm = 2mQRS =
2(90°) = 180°
m = 2mZYX =
Ex. 2: Finding Measures of Arcs and Inscribed Angles
• Find the measure of the blue arc or angle.
ZWX
2(115°) = 230°
XY
Z
W
115˚
m = ½ m
Ex. 3: Finding Measures of Arcs and Inscribed Angles
• Find the measure of the blue arc or angle.NMP
½ (100°) = 50°
NP
P
N
M
100°
Theorem 10.8
• If two inscribed angles of a circle intercept the same arc, then the angles are congruent.
• C D
C
B
A
D
Ex. 4: Finding the Measure of an Angle
• It is given that mE = 75°. What is mF?
• E and F both intercept , so E F. So, mF = mE = 75°
GH
H
G
E
F
75°
Example
68/2 = 34
180-118 = 62
62/2 = 31
62 + 68 = 130
180-68 = 118 118 + 62 = 180
Same as arc QP=62
68 + 62 + 118 = 248
Assignment
• Practice Workbookp. 193(1-15)