The Arcs in a Circle

Multiple Angles in One Circle

Inscribed and Central Angles

AD is twice the measure of the inscribed angle: 2(25) = 50°

A

C

B

DCE = 30° AD =_____ABD = 25°

AB = _____

50°

130°

The sum of a semi-circle is 180°180 – 50 = 130°

DE

DE = ___

EB = _____

A central angle is the same as the arc it creates: DE = 30°

30°

The sum of a semi-circle is 180°EB = 180 – 30 = 150°

150°

30

25

Inscribed and Tangent Angles

AC is twice the measure of the inscribed angle: 2(60) = 120°

A C

B

ABF = 45° AC =_____ABC = 60°

AEB = _____

120°

90°

Arc AEB is twice the measure of the tangent angle.

2(45) = 90°

DE

CDB = _____

Sum of arcs: 120 + 90 = 210 CDB : Subtract sum from 360:360 – 210 = 150°

150°

4560

FG

Note: The other TangentAngle would be half of 150:

Angle CBG = 75°

75

Circles K and L• Look carefully at each problem. Is the arc

created by a central angle? Inscribed?

• Show your work.

• These are due in class.

• If you are missing a quiz/test or did not turn in your notebook, please talk to me about doing that today.