1. LESSON LESSON 11.4 PART I ANGLE MEASURES
OBJECTIVE:
To find the measures of angles formed by chords, secants, and
tangents.

2. REVIEW
Chord:
segment whose endpoints
lie on a circle
Secant:
line that intersects the
circle in two points
line that lies in the plane of a
circle and intersects the circle
in exactly one point
Tangent:

3. m1= 1/2(x + y) Theorem 11-11: (1) The measure of an angle formed by
two lines that intersect
a circle is
INSIDE
1/2 THE SUM OF MEASURES
OF THE INTERCEPTED ARCS.
FORMULA: y x 1
m1= 1/2(x + y)

4. m1 = 1/2(x - y) Theorem 11-11: (1) The measure of an angle formed by
two lines that intersect a
circle is
OUTSIDE
1/2 THE DIFFERENCE OF
MEASURES OF THE
INTERCEPTED ARCS.
FORMULA: 1
m1 = 1/2(x - y) y x

5. Case I Case II Case III 2 secants 1 secant 2 tangents 1 tangent y y yx x y 1 y 1 x

6. EXAMPLES 1.
90º x
46º
x = 1/2( )
x = 68º

7. 2.
95º z
20º
20 = 1/2(95 - z)
40 = 95 - z
-55 = -z
55º = z

8. PRACTICE w 3.
110º
70º
70 = 1/2(w - 110)
140 = w – 110
250º = w

9. 4. y
110º
30º
y = 1/2( )
y = 40º

10. 5.
268º
92º x
x = 1/2( )
x = 88º

11. 6. x
94º
112º
94 = 1/2(x + 112)
94 = 1/2x + 56
38 = 1/2x
76º = x

12. ASSIGNMENT: Page 611
#1-6, 17-19, 27, 38, 41-42