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 ̊ ̊ = 360 ̊ = 360 This means …… = ̊. When we cancel like terms, we see that = 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

Assignment Page 617 #9-17