10-2 Measuring Angles and Arcs day 2

You measured angles and identified congruent angles. Identify central angles, major arcs, minor arcs, and semicircles, and find their measures.

• Find arc lengths.

Arc-Additional TheoremThe measure of two

adjacent, nonoverlapping arcs is the sum of the measures of the two arcs.

That is if C is on arc AB, then mAB = mAC + mCB

A

B

C

p. 708

Find each arc measure.

• mRST

• mDE

• mHGF

R

S

T

D

E

H

G

F

40°

60°

153°

38°

320°

120°

191°

.

Substitution= 58 + 32

Answer:

Arc Addition Postulate

Arc Addition Postulate

Substitution= 90 + 58

= mIMJ + mJMK

= 148

Answer:

A. 180

B. 90

C. 52

D. 38

A. 52

B. 90

C. 142

D. 180

Arc Lengths

Arc lengths are the pieces of the circumference cut by central angles.

Arc lengths are measured in units of measure like inches and centimeters.

Can arc length be measured with a ruler?

Arc length

A

B

p. 709

Formula for Arc Length

360

degreesarc2 rL

is a central angle of ּסK

Find the arc length (L) of JL to the nearest tenth.

C = 2 π r (circumference)

The arc covers 125° out of a total of 360° or

JKL

JK

L

125° 12 cm

360

125

2.26360

125122 L

If the circumference of a circle is 21π, what is the length of a 30° arc?

B

A

C

30°

360

3021 L

5.54

7

12

21

12

121L

Arc Length Equation

Substitution

Answer:

Use a calculator.cm

Arc Length Equation

Substitution

Use a calculator.

Answer:

Arc Length Equation

Substitution

Use a calculator.

Answer:

A. 3.56 cm

B. 3.77 cm

C. 3.98 cm

D. 4.21 cm

A. 36.56 cm

B. 37.79 cm

C. 38.61 cm

D. 40.21 cm

A. 32.99 cm

B. 33.59 cm

C. 33.89 cm

D. 34.61 cm

• What is an arc length?

Arc lengths are the pieces of the circumference cut by central angles.

• How do you find arc length?

360

degreesarc2L r