1. 4. What is the value of x in the following ?
2 b) 4 c) 8 d) 16
5. Which line graphed below has the greatest slope
Line r
Line s
Line t
Line p
Which of the following statements is not true about quadrilaterals?
All squares are rectangles b) All rhombuses are rectangles
All rectangles are parallelograms d) All rhombuses are parallelograms y m l x p n

2. Other Angles
Unit 9 Section 9.6

3. Draw a diagram as an example of each theorem.
Theorem 9-9: The measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arc.

4. Theorem 9-10: The measure of an angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs.
case 1: two secants case 2: two tangents
case 3: a secant and tan

5. Example 1: Find the value of x.
80°
20° x°

6. Example 2: Find the value of x.
160°
140° x°

7. Example 3: Find the value of x.
230°

8. Example 4: Find the value of x.
120°
140°
80°

9. Example 5: Find the value of x.
150° x°
35°

10. Example 6: Find the value of x.
100°
30° x°

11. m< 1 = ____ m< 6 = ____ m< 2 = ____ m< 7 = ____
Example 7: Given that segment BE is a diameter of circle O, measure of arc AB = 80°, measure of arc BC = 20°, and measure of arc DE = 50°.
m< 1 = ____ m< 6 = ____
m< 2 = ____ m< 7 = ____
m< 3 = ____ m< 8 = ____
m< 4 = ____ m< 9 = ____
m< 5 = ____ m< 10 = ____ A B D E 4 1 2 3 9 6 10 7 8 5 O B T C

12. Additional Practice
is tangent to the circle. U
30°
110° W
Complete.
m = ___________
m∠TVS = ___________
m∠RVS = ___________
m = ___________ R V T
100° S

13. Complete.
If m = 105°, then m∠D = _________.
m = _________. A D C B A
20° B
10°

14. For Questions 7-14, is tangent to ⊙O; is a diameter;
m = 100; m = 30; m = 25.
Complete
m∠1 = _______
m∠2 = _______
m∠3 = _______
m∠4 = _______
m∠5 = _______
m∠6 = _______
m∠7 = _______
m∠8 = _______
Homework: Practice Worksheet 9.6 D B 6 C E 8 3 O 5 A F 2 1 4 7
100° G