1. Angles of a Circle
Lesson 1 – 2
Math iii

2. Arc Semicircle A piece of a circle
An arc formed by the diameter of the circle. It splits the circle into two congruent halves.

3. Two semicircles are and
An arc formed by the diameter of the circle. It splits the circle into two congruent halves.
Two semicircles are and

4. Minor arc Major arc Central angle
An arc that is less than a semicircle
Major arc
An arc that is more than a semicircle
Central angle
An angle in which the vertex is the center
of the circle

5. Use the diagram to below to name:
Two semicircles
A minor arc
Two major arcs
An acute central angle
An obtuse central angle
Two congruent arcs

6. The measure of a minor arc is equal to the measure of its central angle. The measure of central angle MOP = 70o The measure of arc MP = 70o.
70o
70o

7. Find the measure of…
Arc PR
Arc RS
Arc PRS
Arc PS

8. Arc Measure Addition

10. Inscribed angle
An angle whose vertex is located on the edge of the circle
The measure of an inscribed angle is equal to half the
measure of its intercepted arc.
EDGE!
40o
80o

11. Find the measure of the arc or angle in blue.

12. If two inscribed angles intersect the same arc, then the angles are congruent

13. What is the measure of Angle F?

14. If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

15. The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc.
EDGE!

16. An angle inscribed in a semicircle is a right angle.

17. Find the values of x, y, and z in the circle below.xo yo
55o zo

18. State the indicated degree measure.
Arc VW
Angle W
Arc VX
Angle WVX
Arc XW
70o

19. The measure of an angle formed by two chords that intersect inside a circle, is equal to half the sum of the measures of the two intercepted arcs.
INSIDE! 1

20. Find the measure of Angle x.

21. The measure of an angle formed by two secants, two tangents, or a tangent and a secant drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs
Tangent and Secant
Two secants
Two tangents
OUTSIDE!

22. Find the measure of Angle x.

23. Find the measure of 1 and 2.

24. Use the figure to find the measure of the following.
Arc WT
TVS
RVS
Arc RS
110o
30o
100o

25. Given: AB is a tangent, AF is a diameter, arc AG = 100, Arc CE = 30, Arc EF = 25. Find 1, 2, 3, 4, 5, 6, 7, 8 6 8 3 5 2 1 4 7