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Geometry Name: _______________________________________ ____o Date: __________ Quiz 12-4 - 12-5: Circles In Exercises 1–4, fill in the blanks to complete each theorem. 1. If a quadrilateral is inscribed in a circle, then its opposite angles are _____________________. 2. If inscribed angles of a circle intercept the same arc, then the angles are _____________________. 3. The measure of an inscribed angle is _____________________ the measure of its intercepted arc. 4. An inscribed angle has a semicircle for an intercepted arc if and only if the angle is a _____o. Find each measure. mBAC __________ 5. mFE mIHJ __________ 6. mGH __________ __________ Find each value. 7. 9. x __________ mVUS __________ z __________ 8. mZWY __________ 10. Find the angle measures of each inscribed quadrilateral. 11. mB __________ mC __________ mD __________ mE __________ 12. mF __________ mG __________ mH __________ mI __________ 13. Iyla has not learned how to stop on ice skates yet, so she just skates straight across the circular rink until she hits a wall. She starts at P, turns 75° at Q, and turns 100° at R. Find how many degrees Iyla will turn at S to get back to her starting point. _________________________ In Exercises 14-16, match the letter of the drawing to the formula for finding the measure of the angle. 14. mABC 15. mABC 1 2 1 2 mAC mDE _________ A. mAC mDE _________ B. _________ C. 1 16. mABC mAB 2 Find each measure. 17. mFGH ___________ 18. mIJ ___________ 20. 19. mQPR mYUV ________ ________ 21. Some cities in Europe are thousands of years old. Often the small center of the old city is surrounded by a newer “ring road” that allows traffic to bypass the old streets. The figure shows a circular ring road and two roads that provide access to the old city. Find mCBD. Find the value of x. 22. ____________ 23. ___________ ____________ Complete Exercises 24-26 in order to find mECF. 24.Find mDHG. (Hint: DF is a straight segment.) ____________ 25. Find mEF . ____________ 26. Find mECF. ____________