4. What is the value of x in the following ?

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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

Other Angles Unit 9 Section 9.6

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.

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

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

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

Example 3: Find the value of x. 230°

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

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

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

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

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

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

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