1-4 Practice C Pairs of Angles

Name
LESSON
1-4
Date
Class
Practice C
Pairs of Angles
Draw your answers in the space provided.
1. Draw two intersecting lines and label the resulting
angles with the numbers 1, 2, 3, and 4.
2. Label ⬔1 with x. ⬔1 and ⬔2 are supplementary.
Find the measure of ⬔2 and label the diagram.
3. ⬔3 is also supplementary to ⬔2. Find the measure of ⬔3 and label the diagram.
4. From your work in Exercises 1–3, make a conclusion about the measures
of the vertical angles.
5. ⬔X is complementary to ⬔Y, and ⬔Z is also complementary to ⬔Y.
Explain why ⬔X and ⬔Z are congruent.
Adjacent angles are defined as two angles in the same plane with a common
vertex and a common side, but no common interior points.
6. ⬔ADB and ⬔CDB are adjacent angles. If the phrase “but no common interior
points” was not part of the definition, name another pair of angles that would
qualify as adjacent.
Draw your answer in the space provided.
7. Draw a diagram that shows why the
definition of adjacent angles includes
the phrase “in the same plane.”
Use the figure for Exercises 8 –10.
This diagram shows a ray of light reflecting off a mirror.
When light reflects, the incident angle and the reflected
angle are congruent, that is, ⬔1 ⬔2. Find the measure
of ⬔1 in each situation below.
8. ⬔1 ⬔3
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All rights reserved.
9. ⬔3 is a right angle
29
10. m⬔1 2m⬔3
Holt Geometry
LESSON
1-4
Practice A
1-4
Complete the statements.
side
, but no common interior points.
Use the figures for Exercises 3 and 4.
90
4. complement of ⬔Y
.
right angle
Supplementary
measure of the angle.
.
132
6. An angle is its own complement. Find the measure of a supplement to this angle.
angles are two angles whose measures
135
have a sum of 180.
6. The kind of angle formed by the noncommon sides of two adjacent and
straight angle
supplementary angles is a
7. ⬔DEF and ⬔FEG are complementary. m⬔DEF (3x 4)°, and m⬔FEG (5x 6)°.
Find the measures of both angles. m⬔DEF
.
Draw your answer in the space provided.
8. Sketch ⬔1 and ⬔2 so that
they form a linear pair.
Find the measures of both angles. m⬔DEF
9. Name a pair of vertical angles.
Possible answers: ⬔1 and ⬔3
In an equilateral triangle, all three sides have equal lengths
and all three angles have equal measures. Find the measure
of the following angles.
9. supplement of ⬔A
120
30
or ⬔2 and ⬔4
10. Name a linear pair of angles.
Possible answers: ⬔1 and ⬔2; ⬔2 and ⬔3; ⬔3 and ⬔4; or ⬔1 and ⬔4
!
11. ⬔ABC and ⬔CBD form a linear pair and have
equal measures. Tell if ⬔ABC is acute, right,
or obtuse.
Draw your answer in the space provided.
11. Sketch ⬔1 and ⬔2 so that
they are vertical angles.
91; m⬔FEG 89
Use the figure for Exercises 9 and 10.
In 2004, several nickels were minted to commemorate the Louisiana
Purchase and Lewis and Clark’s expedition into the American West. One
nickel shows a pipe and a hatchet crossed to symbolize peace between
the American government and Native American tribes.
3AMPLEANSWER
10. complement of ⬔A
29; m⬔FEG 61
8. ⬔DEF and ⬔FEG are supplementary. m⬔DEF (9x 1)°, and m⬔FEG (8x 9)°.
3AMPLEANSWER
7. Sketch ⬔1 and ⬔2 so that
they are adjacent angles.
3AMPLEANSWER
27
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Geometry
LESSON
1-4
Pairs of Angles
1. Draw two intersecting lines and label the resulting
angles with the numbers 1, 2, 3, and 4.
2. Label ⬔1 with x . ⬔1 and ⬔2 are supplementary.
Find the measure of ⬔2 and label the diagram.
45°; 45°
28
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Practice C
Draw your answers in the space provided.
right
__›
12. ⬔KLM and ⬔MLN are complementary. LM
bisects ⬔KLN. Find the measures of ⬔KLM
and ⬔MLN.
1-4
:
(110 8x)
5. An angle measures 12 degrees less than three times its supplement. Find the
4. The kind of angle formed by the noncommon sides of two adjacent and
complementary angles is a
9
X 137.9
3. supplement of ⬔Z
3. Complementary angles are two angles whose measures have a sum of
LESSON
180
___›
QR
2. Name the ray that ⬔PQR and ⬔SQR share.
2. A linear pair is a pair of adjacent angles whose noncommon sides
are opposite rays.
5.
Pairs of Angles
1. ⬔PQR and ⬔SQR form a linear pair. Find the sum of their measures.
vertex
1. Adjacent angles are two angles in the same plane with a common
and a common
Practice B
LESSON
Pairs of Angles
Holt Geometry
Review for Mastery
Pairs of Angles
Angle Pairs
3AMPLEANSWER
X X X Adjacent Angles
have the same vertex and
share a common side
Linear Pairs
adjacent angles whose
noncommon sides are
opposite rays
Vertical Angles
nonadjacent angles formed
by two intersecting lines
3. ⬔3 is also supplementary to ⬔2. Find the measure of ⬔3 and label the diagram.
4. From your work in Exercises 1–3, make a conclusion about the measures
of the vertical angles.
The measures of the vertical angles are equal.
⬔1 and ⬔2 are adjacent.
5. ⬔X is complementary to ⬔Y, and ⬔Z is also complementary to ⬔Y.
Explain why ⬔X and ⬔Z are congruent.
⬔3 and ⬔4 are adjacent
and form a linear pair.
⬔5 and ⬔6 are vertical
angles.
Tell whether ⬔7 and ⬔8 in each figure are only adjacent, are adjacent and form a
linear pair, or are not adjacent.
If m⬔X m⬔Y 90 and m⬔Z m⬔Y 90, then m⬔X and m⬔Z
2.
1.
are both equal to 90 m⬔Y. So m⬔X m⬔Z. Two angles whose
measures are equal are congruent.
Adjacent angles are defined as two angles in the same plane with a common
vertex and a common side, but no common interior points.
adjacent and form
a linear pair
6. ⬔ADB and ⬔CDB are adjacent angles. If the phrase “but no common interior
points” was not part of the definition, name another pair of angles that would
qualify as adjacent.
3.
only adjacent
not adjacent
Tell whether the indicated angles are only adjacent, are adjacent and
form a linear pair, or are not adjacent.
Possible answer: ⬔ADB and ⬔ADC
only adjacent
4. ⬔5 and ⬔4
Draw your answer in the space provided.
7. Draw a diagram that shows why the
definition of adjacent angles includes
the phrase “in the same plane.”
5. ⬔1 and ⬔4
not adjacent
6. ⬔2 and ⬔3
adjacent and form a linear pair
Use the figure for Exercises 8 –10.
This diagram shows a ray of light reflecting off a mirror.
When light reflects, the incident angle and the reflected
angle are congruent, that is, ⬔1 ⬔2. Find the measure
of ⬔1 in each situation below.
8. ⬔1 ⬔3
9. ⬔3 is a right angle
60
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
45
29
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Name each of the following.
7. a pair of vertical angles
10. m⬔1 2m⬔3
8. a linear pair
Possible answers:
⬔1 and ⬔6, ⬔2 and ⬔5
Possible answers: ⬔1 and ⬔2;
⬔1 and ⬔5; ⬔5 and ⬔6; ⬔6 and ⬔2
72
9. an angle adjacent to ⬔4
Holt Geometry
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
65
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⬔3
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Holt Geometry
Holt Geometry
3/23/07 2:36:22 PM

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