Rochester City School District / Overview



Name ______________________________Module 5 Central Angles and Inscribed AnglesLearning Target: I can use relationships among central angles, inscribed angles, and the intercepted arcs.Opening ExerciseIn the diagram below of circle O, chords AD and BC intersect at E. If m∠DEB=120°, determine the measure of the following angles.27724619065300m∠CEA=__________m∠CED=__________m∠BEA=__________Central Angles and Inscribed AnglesA central angle is an angle whose vertex is the center of a circle. An arc is an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them.401891540005001. AC is the diameter of circle F. Find the measure of each arc.mED = _______mAE = _______mADC = _______mDC = _______mEC = _______Within a circle or congruent circles, congruent arcs are two arcs that have the same measure. In the figure ST?UV.2. Find the measure of each of the following in circle A.417703012509500mBC = _______mBEC = _______m∠BAC = _______m∠BAD = _______mCD = _______An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted arc consists of endpoints that lie on the sides of an inscribed angle and all the points of the circle between them. Theorem 20113240003. Find each measure. m∠PRU = _______mPS = _______201368674549004. Find each measure. m∠LJM = _______m∠LKM = _______mLM = _______Theorem5. Solve for a.1800225167640006. Find each measure. m∠KGH = _______m∠GHJ = _______mKJH = _______mJKG = _______Name ______________________________Module 5 Central Angles and Inscribed AnglesProblem Set3832606165888001. JM and KN is the diameters of circle P. Find the measure of each arc.mJK = _______mJKL = _______mKJN = _______mKM = _______mKJM = _______3971925124460002. Find each measure. m∠DAE = _______mADC = _______mAC = _______3. Find each measure.36889958763000 m∠EDF = _______m∠EGF = _______mEF = _______4. AB is a diameter of the circle shown. The radius is 12.5 cm, and AC=7 cm. 418401517589500Find m∠C. Find AB.Find BC.5. 42468801270000In the circle shown, BC is a diameter with center A. a. Find m∠DAB.b. Find m∠BAE.c. Find m∠DAE.6. In the figure below, O is the center of the circle, and AD is a diameter.46062903492500a. Find m∠AOB.b. If m∠AOB∶m∠COD=3∶4, what is m∠BOC?7. ∠CBD is inscribed in CD and ∠CAD is a central angle that intercepts the same arc. Prove that y=2x.8. Determine the value of x.9. Determine the value of x.10. Find the angle measure of angle x.11. 38338121460500Given circle A, find the following angles of measure.a. m∠BADb. m∠CABc. mBC mBD mBCD 12. In the diagram below, quadrilateral JUMP is inscribed in a circle.27933657302500Opposite angles J and M must be1)right2)complementary3)congruent4)supplementary13. In the accompanying diagram, quadrilateral ABCD is inscribed in circle O. If mAB=132 and mBC=82, find m∠ABC.Name ______________________________Module 5Central Angles and Inscribed AnglesExit Ticket1. The center of the circle below is ?. If angle ? has a measure of 15 degrees, find the values of ? and ?. Explain how you know.2. Find the measure of angles ? and ?. Justify your reasoning.3. Given circle A with diameters BC and DE and mCD=56°.A. What is the measure of ∠CAD?B. What is the measure of ∠CBD?C. What is the degree measure of CBD? ................
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