Download 12-4 Practice B

Name _______________________________________ Date __________________ Class __________________
12-4 Practice B
Inscribed Angles
Find each measure.
1.
mCED  _________
mDEA 
3.
mGH 
_________
mQRS  _________
mTSR 
mFGI  _________
2.
_________
mXVU  _________
4.
mVXW  _________
_________
5. A circular radar screen in an air traffic control
tower shows these flight paths. Find mLNK.
___________
Find each value.
6.
7.
mCED  ________
8.
y  ________
a  ________
9.
mSRT  _______
Find the angle measures of each inscribed quadrilateral.
10.
12.
mX  ________
11.
mC  ________
mY  ________
mD  ________
mZ  ________
mE  ________
mW  ________
mF  ________
mT  ________
13.
mK  ________
mU  ________
mL  ________
mV  ________
mM  ________
mW  ________
mN  ________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry
Name _______________________________________ Date __________________ Class __________________
shaped curve. Start with a circle, O, and
draw one diameter. The nephroid is
then generated by the set of circles
whose centers are on circle O and that
intersect the chosen diameter in exactly
one point. (Circles are tangent to the
chosen diameter.)
m
m

2
 
m 720  sin   cos  2  . Notice that this
equation is independent of the radius r.
Using trial and error with this equation
shows that the measure of a central
angle whose segment has half the area
of the sector is between 108° and 109°.
2. 180°
3. 9.08 cm2
4. 414.69 ft2
5. Possible answer: The length of an arc
with central angle measure m in a circle
 m 


with radius r is equal to 2r  360  . Set
 m 


this equal to the radius: 2r  360   r.
180
This simplifies to m   . The
measure of the central angle is 57.3°.
6. 6 times
7. 60.4%
3. 4.0 ft
2. 9 ft
2
4. 78.6 mm2
5. D
7. A
6. H
8. H
Reading Strategies
1. 4.5 cm2  14.14 cm2
64 2
ft  67.02 ft2
3
3. 10.27 in2
1. 7 cm2; 21.99 cm2
2. 27 in2; 84.82 in2
4. 5.80 m2
5. 11 in.; 34.56 in.
6. 7 cm; 21.99 cm
in.
1. 366.5 cm2
2.
Reteach
3. 1.14 in2
Problem Solving
5.
4. 41.10 yd2
10
 mm  10.47 mm
3
6. 2 cm  6.28 cm
7. 4 in.; 12.57
9
8. 10  or 0.9 mm; 2.83 mm
Challenge
1.
INSCRIBED ANGLES
Practice A
1. supplementary
2. congruent
3. half
4. right angle
5. 30°; 140°
6. 45°; 40°
7. 15
8. 15
9. 42°
10. 71°
11. 120°; 90°; 60°; 90°
12. 130°; 100°; 50°; 80° 13. 105°
2. Conjectures may vary. The length of the
cardioid is in fact eight times the
diameter of circle O.
3. Check students’ work.
4. The term nephroid comes from the
Greek word nephros, which means
“kidney.” The nephroid is a kidney-
Practice B
1. 33°; 192°
2. 9°; 78°
3. 130°; 138°
5. 73°
4. 10°; 90.5°
6. 48°
7. 13
8. 6
9. 77°
10. 71°; 109°; 109°; 71°
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry
Name _______________________________________ Date __________________ Class __________________
11. 90°; 90°; 90°; 90°
12. 68°; 95°; 112°; 85°
13. 59°; 73°; 121°; 107°
Practice C
1. Possible answer: It is given that
AC  AD. In a circle, congruent chords
intercept congruent arcs, so
ABC  AED. DC is congruent to itself
by the Reflexive Property of
Congruence. By the Arc Addition
Postulate and the Addition Property of
Congruence, ACD  ADC. ABC
1
intercepts ADC , so mABC  m
2
ADC . AED intercepts ACD , so
1
mAED  m ACD . By substitution,
2
mABC  mAED. Therefore ABC 
AED.
2. Possible answer: It is given that
PQ  RS. By the definition of congruent
arcs, m PQ  m RS . PSQ intercepts
PQ , and RQS intercepts RS . So
mPSQ must equal mRQS.
Therefore PSQ  RQS. PSQ and
RQS are congruent alternate interior
angles of QR and PS. So QR PS.
3. cannot be inscribed in a circle
4. Can be inscribed in a circle; possible
answer: The two congruent angles of
the kite are opposite, so they must be
right angles. Draw a diameter. Draw
segments from opposite ends of the
diameter to any point on the circle. Use
the compass to copy one of the
segments across the diameter. Draw
the fourth side.
trapezoid inscribed in a circle must be
congruent. Draw any inscribed angle.
Use the compass to copy the arc that
this angle intercepts. Mark off the same
arc from the vertex of the inscribed
angle. Connect the points.
6. cannot be inscribed in a circle
Reteach
1. mLMP  18°; m MN  96°
2. mGFJ  55°; m FH  72°
3. 16.4
4. 45°
5. 70°; 88°; 110°; 92°
6. 120°; 75°; 60°; 105°
7. 132°; 90°; 48°; 90°
8. 101°; 86°; 79°; 94°
Challenge
1. chord; inscribed
2. a. 45°
b. 67.5°
c. 180  11.25n
d. 0  n  16  16


2 n 
180  1 
 ,
p 


p p
n 
2 2
where 0  n 
e. 180 
360 n
, or
p
f. Answers will vary. Students may
choose any values of n and p for
n 5

which p 12 . Sample answer: n 
15, p  36
Problem Solving
1. 160°
2. 112°; 52°; 68°; 128°
3. C
4. G
5. Can be inscribed in a circle; possible
answer: The pairs of base angles of a
5. B
6. G
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry