EXAMPLE 1 Find measures of arcs

RSa. RTSb. RSTc.

SOLUTION

RS is a minor arc, so mRS = m RPS = 110o.a.

RTS is a major arc, so mRTS = 360o 110o = 250o.b. –

Find the measure of each arc of P, where RT is a diameter.

c. RT is a diameter, so RST is a semicircle, and mRST = 180o.

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

EXAMPLE 2 Find measures of arcs

b. mACD = mAC + mCD= 137o + 83o

= 220o

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

SOLUTION

b. mACD

EXAMPLE 2 Find measures of arcs

mADC mAC= 360o – c.

= 360o – 137o

= 223o

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

SOLUTION

c. mADC

EXAMPLE 2 Find measures of arcs

d. mEBD = 360o – mED

= 360o – 61o

= 299o

d. mEBD

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

SOLUTION

GUIDED PRACTICE for Examples 1 and 2

Identify the given arc as a major arc, minor arc, or

semicircle, and find the measure of the arc.

TQ is a minor arc, so m TQ = 120o.

GUIDED PRACTICE for Examples 1 and 2

1. TQ

SOLUTION

. QRT2

SOLUTION

QRT is a major arc, so m QRT= 240o.

GUIDED PRACTICE for Examples 1 and 2

. TQR3

SOLUTION

TQR is a semicircle, so m TQR = 180o.

. QS4

SOLUTION

QS is a minor arc, so m QS = 160o.

GUIDED PRACTICE for Examples 1 and 2

. TS5

SOLUTION

TS is a minor arc, so m TS = 80o.

. RST6

SOLUTION

RST is a semicircle, so m RST = 180o.