Aim: How do we find angle measurements inside and outside of circles?

Aim: How do we find angle measurements inside and outside of circles? Do now: A security camera located at point S views part of a circular area by rotating 30o. How many degrees of the circle’s circumference does the camera observe? 60o 60o 30o S

If… If… a = 70o, then b = 140o a = 70o, then b = 70o a = 36o, then b = 36o a = 36o, then b = 72o An angle inscribed in a semicircle (diameter) is a right angle. b = 170o, then a = 170o b = 170o, then a = 85o Basic angles 1. Central angles 2. Inscribed angles b a b a a = b a = ½ b

If… a = 80o, then x = 40o a = 228o, then x = 114o x = 25o, then a = 50o Special angles Group 1: Tangent - Chord Mnemonic a a x x x = ½ a Since a = 180o, x = 90o. x = ½ a.

If… a = 100o and b = 60o, then x = 20o b = 60o and x = 25o, then a = 110o a = 70o and x = 10o, then b = 50o Special angles Group 2: Secant - Secant Tangent - Tangent Tangent - Secant a b x a b x x b a x = ½ (a - b) Mnemonic

If… a = 90o and b = 10o, then x = 50o b = 100o and x = 70o, then a = 40 o a = 200o and x = 150o, then b = 100o Special angles Group 3: Chord - Chord Mnemonic a Review x b The three formulas: x = ½ a x = ½ (a-b) x = ½ (a+b) x = ½ (a + b)

Putting it all together 60o A Given: In circle O, angle AOB = 60o, angle BEA = 80o, and BOD is a diameter. Find: Arc AB Angle AOD Arc AD Arc CD Arc BC Angle BCA Angle BEC Angle CBE B 50o 120o 80o 60o 100o E 120o 80o O 30o D C 100o

Regents problems 96o 96o 48o

180o = 20o 9 AC: 20o x 7 = 140o BC: 20o x 2 = 40o x = ½ (a - b) x = ½ (140o - 40o) x = ½ (100o) x = 50o Regents problems m arc ACB = 180o a b x m angle CPA = 50o

Aim: How do we find angle measurements inside and outside of circles?