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1-4
1-4 Pairs
PairsofofAngles
Angles
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Geometry
Holt
McDougal
Geometry
1-4 Pairs of Angles
Warm Up
Simplify each expression.
1. 90 – (x + 20)
70 – x
2. 180 – (3x – 10) 190 – 3x
Write an algebraic expression for each of
the following.
3. 4 more than twice a number 2n + 4
4. 6 less than half a number
Holt McDougal Geometry
1-4 Pairs of Angles
Objectives
Identify adjacent, vertical,
complementary, and supplementary
angles.
Find measures of pairs of angles.
Holt McDougal Geometry
1-4 Pairs of Angles
Many pairs of angles have special
relationships. Some relationships are
because of the measurements of the
angles in the pair. Other relationships are
because of the positions of the angles in
the pair.
Holt McDougal Geometry
1-4 Pairs of Angles
Holt McDougal Geometry
1-4 Pairs of Angles
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.
1) AEB and BED
AEB and BED have a common vertex, E, a common
side, EB, and no common interior points. Their
noncommon sides, EA and ED, are opposite rays.
Therefore, AEB and BED are adjacent angles and
form a linear pair.
Holt McDougal Geometry
1-4 Pairs of Angles
Example 1B: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.
2) AEB and BEC
AEB and BEC have a common vertex, E, a
common side, EB, and no common interior points.
Therefore, AEB and BEC are only adjacent angles.
Holt McDougal Geometry
1-4 Pairs of Angles
Describe the angle
relationship
3
2 1
4
3) <1 and <2 …..
adjacent
4) <2 and <4 …..
neither
5) <1 and <3 …..
Linear pair & adjacent
Holt McDougal Geometry
1-4 Pairs of Angles
Holt McDougal Geometry
1-4 Pairs of Angles
 You can find the complement of an angle
that measures x° by subtracting its
measure from 90°, or (90 – x)°.
 You can find the supplement of an angle
that measures x° by subtracting its
measure from 180°, or (180 – x)°.
Holt McDougal Geometry
1-4 Pairs of Angles
Example 2: Finding the Measures of Complements
and Supplements
Find the measure of each of the following.
6. complement of F
(90 – x)
90 – 59 = 31
7. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Holt McDougal Geometry
1-4 Pairs of Angles
Check It Out! Example 2
Find the measure of each of the following.
8. complement of E
(90 – x)°
90° – (7x – 12)° = 90° – 7x° + 12°
= (102 – 7x)°
9. supplement of F
(180 – x)
180 – 116.5° =
Holt McDougal Geometry
1-4 Pairs of Angles
10) An angle is 10° more than 3 times the measure
of its complement. Find the measure of the
complement.
Step 1
compliment
Holt McDougal Geometry
1-4 Pairs of Angles
10) An angle is 10° more than 3 times the measure
of its complement. Find the measure of the
complement.
Step 1
Step 2 Write and solve an equation.
x+ [3(x) + 10] = 90
x + 3x + 10 = 90
4x + 10 = 90
4x = 80
x = 20
The measure of the complement, is 20.
Holt McDougal Geometry
1-4 Pairs of Angles
11) An angle’s measure is 12° more than
the measure of its supplement. Find the
measure of the angle.
“the angle”
Holt McDougal Geometry
1-4 Pairs of Angles
11) An angle’s measure is 12° more than
the measure of its supplement. Find the
measure of the angle.
é1
ù
x + ê x +12ú =180
ë2
û
56
2 3
x = 168 2
3 2
1
3
1
x + x +12 =180
2
x =112
2
1
x + x =168
2
2
“the angle”=
“the angle”= 68°
Holt McDougal Geometry
1-4 Pairs of Angles
Vertical angles are two nonadjacent angles
formed by two intersecting lines.
1 and 3 are vertical angles, as are 2 and 4.
Holt McDougal Geometry
1-4 Pairs of Angles
12. Name the pairs
of vertical angles.
HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Holt McDougal Geometry
1-4 Pairs of Angles
13. Are there any vertical angles in
this picture? If there are, name them.
No, there are not.
Holt McDougal Geometry