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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.
mBAC  __________
5.
mFE 
mIHJ __________
6.
mGH 
__________
__________
Find each value.
7.
9.
x  __________
mVUS  __________
z  __________
8.
mZWY  __________
10.
Find the angle measures of each inscribed quadrilateral.
11.
mB  __________
mC  __________
mD  __________ 
mE  __________
12.
mF  __________

mG  __________
mH  __________
mI  __________

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. mABC 
15. mABC 
1
2
1
2
mAC  mDE 
_________
A.
mAC  mDE 
_________
B.
_________
C.
1
16. mABC  mAB
2
Find each measure.
17. mFGH 
___________
18. mIJ 
___________
20.
19.
mQPR 
mYUV  ________
________
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 mCBD.
Find the value of x.
22.
____________
23.
___________
____________
Complete Exercises 24-26 in order to find mECF.
24.Find mDHG. (Hint: DF is a straight segment.)
____________
25. Find mEF .
____________
26. Find mECF.
____________