Unit Circles
Geometry 2
Day 4 Inscribed Angles
Name: _______________________________
Period: 1 2 3 4 5 6 7 8
Central Angle:
O
Given that P is the center:
𝑚∠𝑂𝑃𝑄 = 𝑚𝑂𝑄
Example: If 𝑚∠𝑂𝑃𝑄 = 120°, what is the
measure of arc OQ?
●P
̅̅̅̅ and 𝑄𝑃
̅̅̅̅?
What is true about 𝑂𝑃
Q
Inscribed Angle:
An inscribed angle has its vertex on the circle and its sides
contain chords of the circle
Practice:
Given: C is the center of the circle and measure or arc LJ = 70°
Is it possible to find the following measurements, if so calculate:
K
L
C
a. m∠𝐿𝐶𝐽 =
b. m∠𝐿𝐽𝐶 =
J
c. m∠𝐶𝐿𝐽 =
d. m∠𝐿𝐾𝐽 =
e. m∠𝐾𝐿𝐽 =
f. m∠𝐾𝐽𝐿 =
Applying the concept
Example 1:
a) If mJKL = 27°, what is mJCL ?
b) If mJCL = 90°, what is mJKL ?
K
K
L
C
L
C
J
J
Example 2:
a) What is the mWTV ?
b) What is the mTVU ?
T
76°
T
76°
U
T
80°
65°
65°
W
c) What is the mWTV ?
W
58°
U
W
110
110
U
115
V
V
V
Example 3:
a) What is the measure of MRS ?
b) What is the measure of RST ?
M
M
45º
54º
S
S
36º
27º
T
T
R
R
Example 4: Find the value of x
B
a)
B
b)
A
47°
71°
65°
C
A
x
64°
x
58°
x
55°
B
c)
C
A
C