Lesson 10 6 Theorem 10 12 If two

Lesson 10 -6 • Theorem 10. 12 If two secants intersect in the interior of a circle, then the measure of an angle formed is one-half the sum of its measure of the arcs intercepted by the angle and its vertical angle.

Lesson 10 -6 (con’t) • Theorem 10. 13 If a secant and tangent intersect at a point of tangency, then the measure of each angle formed is one-half the measure of the intercepted arc. • Theorem 10. 14 If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

Find Method 1 if and

Method 2 Answer: 98

Find if Answer: 138 and

Find Answer: 55 if and

Find Answer: 58 if and

Find x. Theorem 10. 14 Multiply each side by 2. Add x to each side. Subtract 124 from each side. Answer: 17

Find x. Answer: 111

JEWELRY A jeweler wants to craft a pendant with the shape shown. Use the figure to determine the measure of the arc at the bottom of the pendant. Let x represent the measure of the arc at the bottom of the pendant. Then the arc at the top of the circle will be 360 – x. The measure of the angle marked 40° is equal to one-half the difference of the measure of the two intercepted arcs.

Multiply each side by 2 and simplify. Add 360 to each side. Divide each side by 2. Answer: 220

PARKS Two sides of a fence to be built around a circular garden in a park are shown. Use the figure to determine the measure of Answer: 75

Find x. Multiply each side by 2. Add 40 to each side. Divide each side by 6. Answer: 25

Find x. Answer: 9

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