10.4 Inscribed Angles

1. 10.4 Inscribed Angles What you’ll learn: To find measures of inscribed angles. To find measures of angles of inscribed polygons.

2. Inscribed Angles Inscribed angle – an angle whose vertex is on the circle and whose sides are chords of the circle. Intercepted arc is intercepted by B B A C

3. Theorem 10.5 Inscribed Angle Theorem If an angle is inscribed in a circle, then the measure of the angle equals one-half the measure of its intercepted arc (or the measure of the intercepted arc is twice the measure of the inscribed angle). mB=½ or 2mB= A C B

4. Theorem 10.6 If 2 inscribed angles of a circle (or congruent circles) intercept congruent arcs or the same arc, then the angles are congruent. AC and BD A B C D

5. Theorem 10.7 If an inscribed angle intercepts a semicircle, the angle is right angle. B=90 A B C

6. Theorem 10.8 If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. A+C=180 B+D=180 B A C D

7. In F, =20, =40, =108and = Find the measures of the numbered angles X W Y 3 5 4 2 U 1 Z T

8. Find the measure of each numbered angle. 2=x+9 4=2x+6

9. Homeworkp. 5498-28 even