SECONDARY MATH 2 11.2 – Central and Inscribed Angles

WARM-UP:

Calculate the arc length and area of the sector with the given information.

𝜃 = 210°

𝑟 = 0.5 𝑚𝑖𝑙𝑒𝑠

QUESTIONS ON 11.1

WHAT YOU WILL LEARN

I will be able to find any central angle, inscribed angle, or the measure of any minor or major arc.

KEY WORDSCentral Angle:

Where is the vertex?

What are the sides?

KEY WORDSInscribed Angle:

Where is the vertex?

What are the sides?

KEY WORDSSemicircle:

Major Arc:

Minor Arc:

CENTRAL OR INSCRIBED?

FIND THE MEASURE OF THE ARC

USING CENTRAL ANGLE

Measure of Central Angle = Measure of Intercepted Arc

B

D

C50BCDm

50) ( :Then BDarcmA

MEASURE OF THE ARC (CENTRAL ANGLE)

MEASURE OF THE CENTRAL ANGLE

120°

FIND MEASURE OF THE ARC

A

B

D

USING INSCRIBED ANGLE

Measure of Inscribed Angle = ½ Measure of Intercepted Arc

25BADm

25*2) ( :Then BDarcm

50) ( :Then BDarcm

C

MEASURE OF THE ARC (INSCRIBED ANGLE)

MEASURE OF THE INSCRIBED ANGLE

PRACTICE

INSTRUCTIONS FOR PROBLEMS 16-23

A is the center.

DF is a diameter of the circle.

The length of DF is 20.

The measure of arc EF is 70 degrees.

Find the values for the other arcs and angle measures.