Download angle problems within circle geometry can essentially be c

Name: ___________________________________
Date: _________________
THE ANGLE THEOREMS- DAY 1
GEOMETRY N
All angle problems within circle geometry can essentially be classified into three subcategories: (1)
angles within a circle, (2) angles on a circle, and (3) angles formed outside the circle.
Theorem #1 – Any central angle formed (an angle with its vertex at the center of the circle) has a
measure equal to the arc that it intercepts.
Exercise #1: In the following diagram of circle O it is given that mAOB  112 . Find mAB .
A
O
B
Theorem #2 – An inscribed angle on a circle always measures one-half of its intercepted arc.
Exercise #2: In the figure shown, it is given that mAB  160 .
A
(a) Determine mAOB .
O
(b) Determine mACB .
C
B
Exercise #3: In the figure shown, BAC is the diameter of
A and intersects with tangent ED at C. Find the measure of
BCE .
E
B
.
A
C
D
Theorem #3- The intersection of a radius or a diameter and a tangent always forms a right angle at
the point of tangency.
**NOTE: All of the arcs in a circle sum to 360O.**
1. Find each of the following in circle P.
K
a) mKPV = _________
b) m KZ = _________
c) mSPW = ________
d) m YVK = ________
e) m WSZ = _________
f) SPZ = _________
g)
h) m VWY = ________
Z
S
P
52
V
W
32
Y
m SYK = _________
2. Find mST in Circle P.
S
T
P
c°
(3c–12)°
W
3. Find the missing measurements
128°
a)
mD _________
b) k _________
i°
130°
C
mAB ________
f _________
k°
mBD ________
i _________
mDA ________
e _________
g ________
f°
g°