Download Name an angle pair that satisfies each condition. 1. two acute

Sample answer: Vertical angles are two nonadjacent
angles formed by two intersecting lines. There are
many acute vertical angles in the figure.
and are acute vertical angles.
1-5 Angle Relationships
Name an angle pair that satisfies each condition.
13. two supplementary adjacent angles
SOLUTION: Sample answer: If the sum of the measures of two
adjacent angles is 180, then they are supplementary
adjacent angles. There are many supplementary
adjacent angles in the figure.
and share a common side and vertex, also
.
So,
and are supplementary adjacent angles.
1. two acute vertical angles
SOLUTION: Vertical angles are two nonadjacent angles formed
by two intersecting lines.
15. an angle complementary to
FDG
SOLUTION: Complementary angles are two angles with measures
that have a sum of 90.
Since
is complementary to 17. an angle supplementary to
JAE
SOLUTION: Supplementary angles are two angles with measures
that have a sum of 180.
Since
,
is supplementary to
.
You can use the corner of a piece of paper to see
that ∠ZVY and ∠WVU are less than right angles.
Therefore, and are acute vertical angles.
Find the value of each variable.
Name an angle or angle pair that satisfies each
condition.
19. SOLUTION: In the figure, the
angle and the angle are vertical angles.
Vertical angles are congruent. 9. two acute vertical angles
SOLUTION: Sample answer: Vertical angles are two nonadjacent
angles formed by two intersecting lines. There are
many acute vertical angles in the figure.
and are acute vertical angles.
13. two supplementary adjacent angles
SOLUTION: Sample answer: If the sum of the measures of two
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adjacent angles is 180, then they are supplementary
adjacent angles. There are many supplementary
adjacent angles in the figure.
21. Page 1
SOLUTION: Since (2x + 25)° and (3x – 10)° are vertical angles, they are congruent.
Solve for y.
1-5 Angle
Relationships
23. 21. SOLUTION: Since (2x + 25)° and (3x – 10)° are vertical angles, they are congruent.
SOLUTION: Supplementary angles have measures that sum to
180. So,
and .
Consider
.
Solve for y.
25. ALGEBRA E and F are supplementary. The
measure of E is 54 more than the measure of
F. Find the measures of each angle.
23. SOLUTION: Supplementary angles have measures that sum to
180. So,
and .
Consider
SOLUTION: Supplementary angles are two angles with measures
that have a sum of 180. Then,
. It
is given that
.
Substitute.
.
Substitute
in .
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25. ALGEBRA
E and
F are supplementary. The
27. ALGEBRA The measure of the supplement of an
angle is 40 more than two times the measure of the
complement of the angle. Find the measure of the
angle.
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SOLUTION: Let x be the measure of an angle.
Substitute
in 1-5 Angle Relationships
.
27. ALGEBRA The measure of the supplement of an
angle is 40 more than two times the measure of the
complement of the angle. Find the measure of the
angle.
SOLUTION: Let x be the measure of an angle.
The measure of an angle which is complementary to
angle is
The measure of an angle which is supplementary to
angle is
31. If m LNM = 8x + 12 and m
m JNP.
JNL = 12x – 32, find
SOLUTION: The angles in a linear pair are supplementary. So,
.
and
are vertical angles. Since the vertical angles are congruent,
The measure of an angle is 40. Substitute
in ALGEBRA Use the figure below.
So,
29. If m KNL = 6x – 4 and m LNM = 4x + 24, find
the value of x so that KNM is a right angle.
SOLUTION: In the figure,
Since
is a right angle,
33. PHYSICS As a ray of light meets a mirror, the light
is reflected. The angle at which the light strikes the
mirror is the angle of incidence. The angle at which
the light is reflected is the angle of reflection. The
angle of incidence and the angle of reflection are
congruent. In the diagram below, if m RMI = 106,
find the angle of reflection and m RMJ.
.
31. If m LNM = 8x + 12 and m
m JNP.
JNL = 12x – 32, find
SOLUTION: The angles in a linear pair are supplementary. So,
.
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SOLUTION: The angle of reflection and the angle of incidence are
congruent.
So,
.
In the figure,
.
Substitute.
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In the figure,
Substitute
in 1-5 Angle Relationships
So,
33. PHYSICS As a ray of light meets a mirror, the light
is reflected. The angle at which the light strikes the
mirror is the angle of incidence. The angle at which
the light is reflected is the angle of reflection. The
angle of incidence and the angle of reflection are
congruent. In the diagram below, if m RMI = 106,
find the angle of reflection and m RMJ.
35. ALGEBRA
and intersect at point V. If
m WVY = 4a + 58 and m XVY = 2b – 18, find the
values of a and b so that
is perpendicular to .
SOLUTION: Since
and perpendicular to
intersect at point V and
,
and is SOLUTION: The angle of reflection and the angle of incidence are
congruent.
So,
.
In the figure,
.
Substitute.
The angle of reflection measures 53°.
In the figure,
So, a is 8 and b is 54. Determine whether each statement can be
assumed from the figure. Explain.
35. ALGEBRA
and intersect at point V. If
m WVY = 4a + 58 and m XVY = 2b – 18, find the
values of a and b so that
is perpendicular to .
SOLUTION: Since
and perpendicular to
intersect at point V and
,
and eSolutions
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is 37. 4 and
8 are supplementary.
SOLUTION: Since
and supplementary.
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form a linear pair, they are 1-5 Angle
Relationships
So, a is 8 and b is 54. Determine whether each statement can be
assumed from the figure. Explain.
37. 4 and
8 are supplementary.
SOLUTION: Since
and form a linear pair, they are supplementary.
The answer is “Yes”.
39. SOLUTION: From the figure, ∠3 and ∠6 are adjacent. Since ∠5
is a right angle, ∠3 and ∠6 will be complementary.
This determines that both angles are acute.
However, unless we know that the larger angle was
bisected to form ∠3 and ∠6, the measures of and are unknown. So, we cannot say .
The answer is “No”.
41. 5 and
7 form a linear pair.
SOLUTION: A linear pair is a pair of adjacent angles with noncommon sides that are opposite rays.
and do not form a linear pair, since they are
not adjacent angles.
49. JUSTIFY ARGUMENTS Are there angles that do
not have a complement? Explain.
SOLUTION: Complementary angles are two angles with measures
that have a sum of 90. By definition, the measure of
an angle must be greater than 0. So, each angle must
have a measure less than 90. Thus, each angle in a
complementary pair is an acute angle.
Angles that have a measure greater than or equal to
90 can not have a complement, since the addition of
any other angle measure will produce a sum greater
than 90. Therefore, right angles and obtuse angles do
not have a complement.
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