Measuring Inscribed Angles

Definition of Inscribed Angle

• An inscribed angle is an angle with its vertex on the edge of a circle.

Central Angle and Inscribed Angle capturing the same arc

What is the measure of the central angle?How do we solve for Angle B?

B

120 ̊A central angle has the same measure as the arc it captures.

How do we solve for Angle B?• First, we can turn

this odd shape into two triangles, by adding a radius

• Since all radii are equal, these are two isosceles triangles.

• That means that each triangle has congruent base angles.B

120 ̊

How do we solve for Angle B?

B

120 ̊

• A triangle has 180 .̊• 2 + = 180 ̊ and

2 + = 180 . ̊• A circle has 360 . ̊• + + 120 = 360 . ̊ ̊• 180 +180 = 360• This means ……2 + + 2 + = + + 120

. ̊• When we cancel like terms,

we see that 2 + 2 = 120 ̊• ∡B = + • 2B=120 ̊ or ∡B = ½ 120 ̊

How do we solve for Angle B?

• The measure of an inscribed angle is half the measure of the arc it captures.

•∡B = ½ AC

B

A

C

So…..

Let’s try a few examples

A

B C

∡B =90 ̊

∡F =

Let’s try a few examples

A

B C

53 ̊D

E

F

G

53 ̊

Assignment

Page 617#9-17