1) If a tangent and secant intersect at the point of tangency, the measure of the angle formed is half the measure of the intercepted arc. 2) If two secants or chords intersect in the interior of a circle, the measure of each angle formed is half the sum of the intercepted arcs. 3) If secants or tangents intersect outside a circle, the measure of the angle formed is half the difference between the intercepted arcs.

1. Obj. 58 Angle Relationships
The student is able to (I can):
• Find the measures of angles formed by lines that
intersect circles
• Use angle measures to solve problems

2. If a tangent and a secant (or a chord)
intersect at the point of tangency, then
the measure of the angle formed is half the
measure of its intercepted arc.
F
L
•
Y
LF is a secant.
LY is a tangent.
∠ =
1
m FLY mFL
2

3. Example Find each measure:
1. m∠EFH
2.
180 — 122 = 58º
mGF
∠ = = °
1
m EFH (130) 65
2
58º
= = °mGF 2(58) 116

4. If two secants or chords intersect in the
interior of a circle, then the measure of
each angle formed is half the sum of the
intercepted arcs.
1111
G
R
A
D
( )∠ = +
1
m 1 mDG mRA
2

5. Example Find each measure.
1. m∠1
2. m∠2
m∠2 = 180 — m∠1
= 180 — 80 = 100º
99º
61º
1
2
( )∠ = +
1
m 1 99 61
2
= 80º

6. If secants or tangents intersect outside a
circle, the measure of the angle formed is
half the difference between the intercepted
arcs.
M O N
E
Y
1
( )∠ = −
1
m 1 mNY mOE
2

7. Example Find each measure
1. m∠K
2. x
186º
62º
K
26º
94º
∠ = −
1
m K (186 62)
2
= 62º
= −
1
26 (94 x)
2 xº
52 = 94 — x
x = 42º