Download Angles Formed By Chords

ANGLES FORMED BY CHORDS
Circle Geometry
DO NOW

1.
Find the measure of each exterior angle of a
polygon with 18 sides.

2.
Find the sum of the interior angle measures
of a 20-gon.
PRACTICE

In circle O, the m<DAC = 40, and arc BC is
congruent to arc CD. Find m<BEC.
E
D
A
O
C
B
PRACTICE

Find the m<PQR.
P
Q
T
R
PRACTICE

In circle A, m<1 = 6x + 11, m<2 = 9x + 19,
m<3 = 4y – 25, m<4 = 3y – 9 and arcs PQ and RS
are congruent. Find each of the following:
Q
R
a. m<1
b. m<2
P
A
S
c. m<3
d. m<4
e. arc PQ
T
f. arc PT
g. arc PT
h. arc TS
ANGLES FORMED BY TWO INTERSECTING
CHORDS

When two chords intersect “inside” a circle, four
angles are formed. At the point of intersection, two
sets of vertical angles can be seen in the corners of
the X that is formed on the picture. Remember:
vertical angles are congruent.
A
C
Angle Formed by Two Chords =
E
O
D
½ Sum of Intercepted Arcs
B
m<BED = ½(mAC + mBD)
PRACTICE – SOLVE FOR X

1.
D
80
B
E x
O
112
A
C

2.
A
C
64
D
*O
Q 51
X
H
PRACTICE – SOLVE FOR X

3.
L
Q
x
O
90
22
M
P

4.
T
x
o
M B
35
H
A
PRACTICE – SOLVE FOR X

5. If arc CB : arc DA = 3:5, find arc CB and
arc DA.
C
A
E
100
B
D