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Answers to Think and Discuss
THINK AND DISCUSS
1. All rt. measure 90°, so the
sum of the measures of any 2 rt.
is 180°. Therefore any 2 rt. are supp.
1. Explain why any two right angles are supplementary.
2. Is it possible for a pair of vertical angles to also be adjacent? Explain.
3. GET ORGANIZED Copy and complete the graphic organizer below. In
each box, draw a diagram and write a definition of the given angle pair.
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1-4
2. Vert. cannot be adj. because
the def. of vert. states that
they are nonadj. formed by
intersecting lines.
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3. See p. A2.
Exercises
1-4 Exercises
KEYWORD: MG7 1-4
KEYWORD: MG7 Parent
GUIDED PRACTICE
Assignment Guide
Vocabulary Apply the vocabulary from this lesson to answer each question.
(90 - x)°; 1.
(180 - x)°
Assign Guided Practice exercises
as necessary.
An angle measures x°. What is the measure of its complement? What is the measure
of its supplement?
BC
2. ∠ABC and ∠CBD are adjacent angles. Which side do the angles have in common? 
SEE EXAMPLE
1
p. 28
Tell whether the angles are only adjacent, adjacent
and form a linear pair, or not adjacent.
3. ∠1 and ∠2 adj.;
4. ∠1 and ∠3 not adj.
lin.
pair
5. ∠2 and ∠4
6. ∠2 and ∠3 only adj.
not adj.
SEE EXAMPLE
2
9. supplement of ∠B
SEE EXAMPLE
3
p. 29
SEE EXAMPLE 4
p. 30
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If you finished Examples 1–5
Basic 14–22, 24–30, 33, 34,
37–43, 47–55
Average 14–44, 47–55
Advanced 14–55
Find the measure of each of the following.
7. supplement of ∠A 98.8°
p. 29
(185 - 6x)°
8. complement of ∠A 8.8°
­ÈÝÊÊx®Â
10. complement of ∠B
(95 - 6x)°
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If you finished Examples 1–3
Basic 14–22, 25, 27–30, 34
Average 14–22, 25, 27–35
Advanced 14–22, 25, 27–35, 37
11. Multi-Step An angle’s measure is 6 degrees more
than 3 times the measure of its complement.
Find the measure of the angle. 69°
Homework Quick Check
Quickly check key concepts.
Exercises: 14, 18, 22, 24, 28,
30, 34
12. Landscaping A sprinkler swings back and
forth between A and B in such a way that
∠1 ∠2. ∠1 and ∠3 are complementary,
and ∠2 and ∠4 are complementary.
If m∠1 = 47.5°, find m∠2, m∠3, and m∠4.
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m∠2 = 47.5°; m∠3 = m∠4 = 42.5°
SEE EXAMPLE
p. 30
5
13. Name each pair of vertical angles.
∠ABE, ∠CBD; ∠ABC, ∠EBD
1- 4 Pairs of Angles
ge07se_c01_0028_0033.indd 31
31
8/29/06 9:49:56 AM
KEYWORD: MG7 Resources
Lesson 1-4
31
Exercise 33 involves
using algebra to
find measures of
complementary angles, congruent
angles, and linear pairs. This exercise
prepares students for the Multi-Step
Test Prep on page 34.
PRACTICE AND PROBLEM SOLVING
14–17
18–21
22
23
24
Answers
33a.
1
2
3
4
5
19. complement of ∠A 33.6°
20. supplement of ∠B (184 - 2x)°
21. complement of ∠B (94 - 2x)°
23. Art In the stained glass pattern, ∠1 ∠2.
∠1 and ∠3 are complementary, and ∠2 and
∠4 are complementary. If m∠1 = 22.3°,
find m∠2, m∠3, and m∠4.
H
K
A
J
18. supplement of ∠A 123.6°
22. Multi-Step An angle’s measure is 3 times the measure of its complement.
Find the measure of the angle and the measure of its complement. 67.5°; 22.5°
Application Practice p. S28
b.
J
K
24. Name the pairs
of vertical angles.
A
∠PTU, ∠VTR; ∠UTQ, ∠STV ;
∠QTR, ∠PTS; ∠PTQ, ∠STR;
∠UTR, ∠PTV ; ∠QTV, ∠UTS
H
1
2
+
1
*
4
3
m∠2 = 22.3°; m∠3 = m∠4 = 67.7°
H
c.
£
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Given m∠A = 56.4° and m∠B = (2x - 4)°, find the measure of each of the following.
Skills Practice p. S4
K
Ó
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14. ∠1 and ∠4 adj.; 15. ∠2 and ∠3 adj.; lin. pair
lin. pair
16. ∠3 and ∠4
17. ∠3 and ∠1 not adj.
only adj.
Extra Practice
J
A
Tell whether the angles are only adjacent, adjacent
and form a linear pair, or not adjacent.
Independent Practice
For
See
Exercises Example
/
-
,
6
25. Probability The angle measures 30°, 60°, 120°, and 150° are written on slips of
paper. You choose two slips of paper at random. What is the probability that the
angle measures are supplementary? 1
_
3
Multi-Step ∠ABD and ∠BDE are supplementary. Find the measures of both angles.
26. m∠ABD = 5x°, m∠BDE = (17x - 18)° 45°; 135°
27. m∠ABD = (3x + 12)°, m∠BDE = (7x - 32)° 72°; 108°
28. m∠ABD = (12x - 12)°, m∠BDE = (3x + 48)° 103.2°; 76.8°
32. The measure of
an acute ∠ is less
than 90°. Therefore
the measure of
its supp. must be
between 90° and
180°, which means
the supp. is an
obtuse ∠.
Multi-Step ∠ABD and ∠BDC are complementary. Find the measures of both angles.
29. m∠ABD = (5y + 1)°, m∠BDC = (3y - 7)° 61°; 29°
30. m∠ABD = (4y + 5)°, m∠BDC = (4y + 8)° 43.5°; 46.5°
31. m∠ABD = (y - 30)°, m∠BDC = 2y° 10°; 80°
32. Critical Thinking Explain why an angle that is supplementary to an acute
angle must be an obtuse angle.
33. This problem will prepare you for the Multi-Step Test Prep on page 34. H is in the
interior of ∠JAK. m∠JAH = (3x - 8)°, and m∠KAH = (x + 2)°. Draw a picture of
each relationship. Then find the measure of each angle.
a. ∠JAH and ∠KAH are complementary angles. m∠JAH = 64°; m∠KAH = 26°
b. ∠JAH and ∠KAH form a linear pair. m∠JAH = 131.5°; m∠KAH = 48.5°
c. ∠JAH and ∠KAH are congruent angles. m∠JAH = m∠KAH = 7°
1-4 PRACTICE A
1-4 PRACTICE C
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