central angle 1 = intercepted angle XY(shown in red) *central angle-vertex on center of circle and radii are its legs

**Ex.- if angle 1=107, arc XY=? 107

inscribed angle 2= 1/2 intercepted arc AB(in purple and red) *inscribed angle- vertex on circle and chords are its legs

**Ex.-if arc AB=240, angle 2=? 120

inscribed angle 3= inscribed angle 4 OR angles inscribed in same arc are congruent (in red and green)

**Ex.- if angle 3=47, angle 4=? arc CD=? 47;94

angle 5=90 OR if an angle is inscribed in a semicirclethen it is a right angle

**Ex.-if GI is a semicircle, angle 5=? 90

angle 6+angle 9=180 angle 7+angle 8=180 OR oppisite angles of an inscribed quadrilateral are supplementary

**Ex-if angle 8= 127, angle 6=88, angle 7=? angle 9=? 53;92

Using the theorems above find the following angles and arcs:

arc AB;DC;DE;AE angles 2;3;4;5;6

if arc BC=70 and angle 1=30

angle 1=30 angle2=55 angle3=35 angle4=55 angle5=35 angle6=70

arc AB=110 BC=70 CD=80 DE=30 EA=70

-Jennifer L.