obj. 58 angle relationships
DESCRIPTION
Find the measures of angles created by secant and tangent linesTRANSCRIPT
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
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 mFL2
Example Find each measure:
1. m∠EFH
2.
180 — 122 = 58º
�mGF
∠ = = °1
m EFH (130) 652
58º
� = = °mGF 2(58) 116
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.
1111G
R
A
D
� �( )∠ = +1
m 1 mDG mRA2
Example Find each measure.
1. m∠1
2. m∠2
m∠2 = 180 — m∠1
= 180 — 80 = 100º
99º
61º
12
( )∠ = +1
m 1 99 612
= 80º
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 mOE2
Example Find each measure
1. m∠K
2. x
186º62º
K
26º
94º
∠ = −1
m K (186 62)2
= 62º
= −1
26 (94 x)2 xº
52 = 94 — x
x = 42º