11-4 Exercises
11-4
Exercises
KEYWORD: MG7 11-4
KEYWORD: MG7 Parent
GUIDED PRACTICE
Assignment Guide
Assign Guided Practice exercises
as necessary.
If you finished Examples 1–2
Basic 12–16, 19, 23, 26–32
Average 12–16, 19, 23, 26–32,
46
Advanced 12–16, 19, 23, 26–32,
46, 47
If you finished Examples 1–4
Basic 12–30, 33, 35, 36,
39–42, 48–53
Average 12–44, 48–53
Advanced 12–53
1. Vocabulary A, B, and C lie on P. ∠ABC is an example of an ? angle.
−−−−
(intercepted or inscribed) inscribed
SEE EXAMPLE
Find each measure.
1
2. m∠DEF 39°
p. 773
3. mEG
58°
204°
4. mJKL
ÇnÂ
әÂ
5. m∠LKM 26°
SEE EXAMPLE
p. 774
Homework Quick Check
7. x
Quickly check key concepts.
Exercises: 13, 16, 18, 22, 26
/
™äÂ
112.5
Ê Ê{ÝxÊÊ
ÊÂ
+
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Find each value.
3
*
-
SEE EXAMPLE
xÓÂ
£äÓÂ
6. Crafts A circular loom can be used
for knitting. What is the m∠QTR in
the knitting loom? 110°
2
p. 773
8. y
,
9. m∠XYZ
13
46°
9
­ÇÞÊÊήÂ
8
7
­{ÊÊÈÞ®Â
­ÎÞÊÊÈ®Â
<
Multi-Step Find the angle measures of each quadrilateral.
SEE EXAMPLE 4
p. 775
10. PQRS
*
­xÝÊÊÓä®Â
11. ABCD
+
£äÝÂ
­{âÊÊ£ä®Â
,
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90°; 90°;
140°; 40°
-
70°; 110°;
115°; 65°
­£äÊÊxâ®Â
PRACTICE AND PROBLEM SOLVING
Find each measure.
Independent Practice
For
See
Exercises Example
12–15
16
17–20
21–22
1
2
3
4
™x°ÓÂ
15. m∠GFH 47.6°
™xÂ
278°
14. mEGH
{ÎÂ
13. m∠KMN 47.5°
£Î™Â
Application Practice p. S38
16. Crafts An artist created a stained
glass window. If m∠BEC = 40° and
= 44°, what is m∠ADC? 62°
mAB
Extra Practice
Skills Practice p. S25
776
86°
12. mML
A
E
B
D
C
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Algebra Find each value.
17. y
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18. z
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£äÝ For Exercises 23–25, advise students
to read the words carefully. They
may find it helpful to draw diagrams
as they read the exercises. Some
students may overlook the word legs
in Exercise 24. Ask these students
to consider what part of the right triangle is the diameter of the circle.
20. m∠MPN
Ó
Multi-Step Find the angle measures of each quadrilateral.
21. BCDE
­âÊÊx™®Â
6
22. TUVW
­£xÞÊÊ{®Â
Â
Ê ÊâÊÊ Ê
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80°; 141°
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19. mAB
_
10 2
3
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79°; 86°;
101°; 94°
Critical Thinking
In Exercise 29, students
are not given any angle or
arc measures. Encourage them to
use their prior knowledge of circles
and the given information of “six
equally spaced points” to first find
arc measures.
Tell whether each statement is sometimes, always, or never true.
23. Two inscribed angles that intercept the same arc of a circle are congruent. A
Exercise 29 involves
using the Inscribed
Angle Theorem
to find the measures of inscribed
angles. This exercise prepares students for the Multi-Step Test Prep on
page 806.
24. When a right triangle is inscribed in a circle, one of the legs of the triangle is
a diameter of the circle. N
25. A trapezoid can be inscribed in a circle. S
Multi-Step Find each angle measure.
26. m∠ABC if
m∠ADC = 112°
56°
115°
27. m∠PQR if
= 130°
mPQR
*
29c. Rt.; ∠FBC
is inscribed in a
semicircle, so it
must be a rt. ∠;
therefore FBC
is a rt. .
Answers
,
+
28. Prove that the measure of a central angle subtended by a chord is
twice the measure of the inscribed angle subtended by the chord.
−−
Given: In H JK subtends ∠JHK and ∠JLK.
Prove: m∠JHK = 2m∠JLK
28. By the def. of arc measure, m JK
= m∠ JHK. Also, the measure of
an ∠ inscribed in a is half the
measure of the intercepted arc,
1
so m∠ JLK = __
m∠ JK . Multiplying
2
both sides of the eqn. by 2 gives
2m∠ JLK = m JK . Thus by subst.,
m∠ JHK = 2m∠ JLK.
29. This problem will prepare you for the Multi-Step Test Prep on page 806.
A Native American sand painting could be used to
indicate the direction of sunrise on the winter and
summer solstices. You can make this design by placing
six equally spaced points around the circumference
of a circle and connecting them as shown.
a. Find m∠BAC. 30°
b. Find m∠CDE. 120°
c. What type of triangle is FBC? Why?
A
B
F
C
E
D
11-4 Inscribed Angles
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Lesson 11-4
777