Central Angle An Angle whose vertex is at

Central Angle : An Angle whose vertex is at the center of the circle A Major Arc Minor Arc More than 180° Less than 180° P ACB To name: use 3 letters C AB B <APB is a Central Angle To name: use 2 letters

Semicircle: An Arc that equals 180° E D To name: use 3 letters EDF P F EF is a diameter, so every diameter divides the circle in half, which divides it into arcs of 180°

THINGS TO KNOW AND REMEMBER ALWAYS A circle has 360 degrees A semicircle has 180 degrees Vertical Angles are Equal Linear Pairs are Supplementary

Vertical Angles are Equal

Linear Pairs are Supplementary http: //www. mathopenref. com/linearpair. html 120° 60°

measure of an arc = measure of central angle A E Q m AB = 96° m ACB = 264° m AE = 84° 96 B C

Arc Addition Postulate A C B m ABC = m AB + m BC

Tell me the measure of the following arcs. m DAB = 240 m BCA = 260 D C 140 R 40 100 80 B A

Congruent Arcs have the same measure and MUST come from the same circle or from congruent circles. C B A 45 45 D 110

Classwork • Page 193 #9 -18 You have 15 minutes.

IN Inscribed Angle: An angle whose is on the circle and sides are chords whose the circle of IN SC AN RIB GL ED E ED T EP RC C TE AR vertex

Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle. 1. C T O L YES ; CL

Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle. 2. Q NO; QVR V K R S

To find the measure of an inscribed angle… 160° 80°

http: //www. geogebra. org /en/upload/files/english/ Guy/Circles_and_angles/ Inscribed_Anlge. html

What do we call this type angle? What do How weis do call the we this solve value type for ofof of x? y? angle? The measure of the inscribed angle is HALF the measure of the inscribed arc!! 120 x y

http: //www. geogebra. org/en/upload/f iles/english/Guy/Circles_and_angles/ Inscribed_angle_practice. html

Examples 3. If m JK = 80 , find m <JMK. 40 4. If m <MKS = 56 , find m MS. 112 J K Q M S

If two inscribed angles intercept the same arc, then they are congruent. 72

http: //www. geogebra. org/en/upload /files/english/Guy/Circles_and_ang les/Inscribed_angle_practice. html

Example 5 In J, m<A= 5 x and m<B = 2 x + 9. Q Find the value of x. m<A = m<B 5 x = 2 x+9 x=3 D T A J B U

Classwork: • Page 193 #9 -23 • Page 207 #1 -15

Whatever is left is homework