Inscribed Angles Pick up Purple Paper There is no quiz or test, I didn’t feel like moving desks…

Learning target: Find measures of inscribed angles, and inscribed polygons. In class: notes/exit slip HW: organize notebooks Warm-up 4/15 B 35° A 2cm 1. Find the measure of arc AB 2. Find the arc length of AB

Key Definitions An angle formed by two chords with a vertex on the circle is an inscribed angle. An arc between the intersection of the sides of an inscribed angle and the circle is an intercepted arc. Inscribed Angle Intercepted Arc

Are the following angles circumscribed or inscribed angles?

Inscribed Angle Theorem The measure of an inscribed angle is half the measure of its intercepted arc.

Angle A’s intercepted arc is a semicircle. Since it’s a semicircle, its intercepted arc measure is 180. 𝑚∠𝐴=90°

True False True False True

What are the values of a and b? 𝑚∠𝑃𝑄𝑇= 1 2 𝑚 𝑃𝑇 60= 1 2 a 120= a 𝑚∠𝑃𝑅𝑆= 1 2 (𝑚 𝑃𝑇 +𝑚 𝑇𝑆 ) 𝑏= 1 2 (120+30) 𝑏=75

Find the measure of the numbered angles 𝑚∠1=𝑚∠3=90° 𝑚∠4= 1 2 (60+80) 𝑚∠4=70 𝑚∠2=180−70 𝑚∠2=110

Now You Try! Find the Variables c = 90 p = 90 q = 122