1. Geometry
Section I can find the measure of arcs in a circle give a central angle and a diameter.

3. EXAMPLE 1
Find measures of arcs
Find the measure of each arc of P, where RT is a diameter. RS a.
RTS b.
RST c.
SOLUTION
RS is a minor arc, so mRS = m RPS = 110o. a.
RTS is a major arc, so mRTS = 360o o = 250o. b. – c.
RT is a diameter, so RST is a semicircle, and mRST = 180o.

5. EXAMPLE 2
Find measures of arcs
A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures.
Survey a.
mAC
SOLUTION a.
mAC
mAB = +
mBC
= 29o + 108o
= 137o

6. EXAMPLE 2
Find measures of arcs
A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures.
Survey b.
mACD
SOLUTION b.
mACD = mAC + mCD
= 137o + 83o
= 220o

7. EXAMPLE 2
Find measures of arcs
A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures.
Survey c.
mADC
SOLUTION
mADC
mAC
= 360o – c.
= 360o – 137o
= 223o

8. EXAMPLE 2
Find measures of arcs
A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures.
Survey d.
mEBD
SOLUTION d.
mEBD = 360o – mED
= 360o – 61o
= 299o

10. EXAMPLE 3
Identify congruent arcs
Tell whether the red arcs are congruent. Explain why or why not. a. b.
SOLUTION a.
CD EF because they are in the same circle and mCD = mEF b.
RS and TU have the same measure, but are not congruent because they are arcs of circles that are not congruent.

11. EXAMPLE 3
Identify congruent arcs
Tell whether the red arcs are congruent. Explain why or why not. c.
SOLUTION c.
VX YZ because they are in congruent circles and mVX = mYZ .