1) An inscribed angle is an angle whose vertex lies on a circle and whose sides contain chords of the circle. 2) The measure of an inscribed angle is equal to one-half the measure of its intercepted arc. 3) If two inscribed angles intercept the same arc or congruent arcs, then the angles are congruent.

1. ©
Ma. Guadalupe Robles
ma.guadaluperobles@yahoo.com

2. An inscribed angle is an angle whose vertex
lies on the circle and whose sides contain
chords of the circle.

3. A
C
O

4. A
C
40°O
Blue lines=
Central angle
Red lines=
Inscribed angle
Intercepted
Arc= 40°

5. A
C
40°O
What is the
Measure of
AOC?
Intercepted
Arc= 40°

6. The measure of an inscribed angle is equal
to one-half the measure of its intercepted
arc.

7. A
C
40°O
What is the
Measure of
AOC?
Intercepted
Arc= 40°20°

8. Intercepted
Arc= ?
50°

9. Intercepted
Arc= ?
70°

10. Intercepted
Arc= ?
20°

11. Intercepted
Arc= ?

12. Intercepted
Arc= 180°O
CB
A
Corollary 108.1
An angle inscribed in a
semicircle is a right angle.

13. 25°
O
D
B
C
A
?

14. If two inscribed angles intercept the same
arc or congruent arcs, then the angles
are congruent.

15. 25°
O
D
B
C
A
25°

16. O
D
B
C
A
60°
?

17. Opposite angles of an inscribed
quadrilateral are supplementary.

18. O
D
B
C
A
60°
120 °
110 ° 70 °

19. ? O
DC
A B
45°
?

20. If two arcs of a circle are inscribed between
parallel secants, then the arcs are
congruent.

21. Practice
A
O
GF
E
D
C
B
40°
°

22. Give the measure of the ff:
1) ABC and DEF
2) The intercepted arc HI if GKJ is 34°
3) N if OPQ is 60°
4) TUV if the intercepted angles are
both 50°
5) R if angle S is 32°
6) Angle W if its intercepted arc is 42°
7) The Minor arc if the major arc is
207°
8) Define intercepted arc.
9) Difference of major and minor arc.
10) If the earth spins on its axis at 360°
per year, at what degree is the earth
spinning from January to October?