1. - draw a diameter - make a radius - join diameter and radius -join other end of diameter and radius - put in any angle for one of the angles formed - fill in all angles x x 180 - 2x y y 180 - 2y (180 - 2x) + (180 - 2y) = 180 360 - 2x - 2y = 180 - 2x - 2y = -180 - 2(x + y) = -180 (x + y) = 90

2. xy 360 - x - y 180 - y 2 180 - y 2 180 - x 2 180 - x 2 - place 2 points on lower half - from first point to center, center to other point - first point to top, top to other point - radius to top point - fill in all angles - put in angle measures around center 360 - x - y 2 180 - y 2 180 - x 2 +=

3. - make quadrilateral by joining 4 points on the circle - draw a radius to each point - label 2 equal angles A A A - label 2 equal angles B - label 2 equal angles C - label 2 equal angles D B B C C D D Every quadrilateral has ___ o 360 So 2A + 2B + 2C + 2D = 360 So 2(A + B + C + D) = 360 So (A + B + C + D) = 180

4. - make quadrilateral - make second quadrilateral - label bottom angle A A - label top two angles x and y x y We know A + x = 180 and A + y = 180 Therefore x = y

5. x 41

6. 42 x

7. 54 x

8. x y 70 85