Download Holt McDougal Geometry 1-4

1-4 Pairs of Angles
Flashback
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
GOALS!
Identify adjacent, vertical,
complementary, and supplementary
angles.
Find measures of pairs of angles.
Holt McDougal Geometry
1-4 Pairs of Angles
Draw an example of adjacent angles.
Draw an example of a linear pair.
Holt McDougal Geometry
1-4 Pairs of Angles
Example 1: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.
AEB and BED
Adjacent and form a linear pair
Holt McDougal Geometry
1-4 Pairs of Angles
Example 2: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.
AEB and BEC
Only adjacent
Holt McDougal Geometry
1-4 Pairs of Angles
Example 3: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.
DEC and AEB
Not Adjacent
Holt McDougal Geometry
1-4 Pairs of Angles
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not
adjacent.
5 and 6
Adjacent and form a linear pair
Holt McDougal Geometry
1-4 Pairs of Angles
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not
adjacent.
7 and SPU
Not adjacent
Holt McDougal Geometry
1-4 Pairs of Angles
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not
adjacent.
7 and 8
Not adjacent
Holt McDougal Geometry
1-4 Pairs of Angles
Complementary anglesWhat is the complement of 30⁰?
What is the complement of 44.2⁰?
Holt McDougal Geometry
1-4 Pairs of Angles
Complementary anglesWhat is the complement of 30⁰?
What is the complement of 44.2⁰?
What is the complement of
Holt McDougal Geometry
1-4 Pairs of Angles
Supplementary anglesWhat is the supplement of 30⁰?
What is the supplement of 44.2⁰?
What is the supplement of
Holt McDougal Geometry
1-4 Pairs of Angles
Warm Up
1.) Find the complement of an angle that
measures 30°.
2.) Find the supplement of an angle that
measures 100°.
Holt McDougal Geometry
1-4 Pairs of Angles
Example 4: Finding the Measures of Complements
and Supplements
Find the measure of each of the following.
A. complement of F
(90 – x)
90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Holt McDougal Geometry
1-4 Pairs of Angles
Find the measure of each of the following.
a. complement of E
(90 – x)°
90° – (7x – 12)° = 90° – 7x° + 12°
= (102 – 7x)°
b. supplement of F
(180 – x)
180 – 116.5° =
Holt McDougal Geometry
1-4 Pairs of Angles
Example 3: Using complements and supplements
Find the measure of each of the following.
A. Find the value of b.
63 + b = 90
b = 27
B. Find the value of x
93 + 3x + 18 = 180
X = 23
Holt McDougal Geometry
1-4 Pairs of Angles
Example 6
∠R and ∠S are complementary. If m∠R = 7 + 3x
and m∠S = 2x + 13. What is the value of x.
Find the measure of both angles.
7 + 3x + 2x + 13 = 90
Set up the equation!
Solve for x!
x = 14
Holt McDougal Geometry
R = 49 and 41
1-4 Pairs of Angles
∠DEF and ∠FEG are supplementary. m∠DEF
= 9x + 1 and m∠FEG = 8x + 9. Find the
measure of both angles.
x = 10
Holt McDougal Geometry
∠DEF = 91 and ∠FEG =89
1-4 Pairs of Angles
Example 7: Problem-Solving Application
Light passing through a fiber
optic cable reflects off the walls
of the cable in such a way that
1 ≅ 2, 1 and 3 are
complementary, and 2 and 4
are complementary.
If m1 = 47°, find m2, m3,
and m4.
m2 = 47°, m3 = 43°, and m4 =43°.
Holt McDougal Geometry
1-4 Pairs of Angles
What if...? Suppose m3 = 27.6°. Find m1,
m2, and m4.
Thus m1 = m2 = 62.4°; m4 = 27.6°.
Holt McDougal Geometry
1-4 Pairs of Angles
Assignment:
Page 32 14-21,26-31
Holt McDougal Geometry
1-4 Pairs of Angles
Warm up
The measurement of angle A is 64.1° and
the measurement of angle B is (4x – 30)°.
1.) Find the supplement of angle A.
2.) Find the complement of angle B.
Holt McDougal Geometry
1-4 Pairs of Angles
Day 2 Vertical Angles
Holt McDougal Geometry
1-4 Pairs of Angles
Holt McDougal Geometry
1-4 Pairs of Angles
Vertical angles
Name two sets of vertical angles
A and C are vertical angles, as are B and D.
What do you know about ∠A and ∠C?
What do you know about ∠B and ∠D?
Holt McDougal Geometry
1-4 Pairs of Angles
Lesson Quiz: Part I
mA = 64.1°, and mB =(4x – 30)°. Find the
measure of each of the following.
1. supplement of A 115.9°
2. complement of B (120 – 4x) °
3. Determine whether this statement is true or
false. If false, explain why. If two angles are
complementary and congruent, then the measure
of each is 90°.
False; each is 45°.
Holt McDougal Geometry
1-4 Pairs of Angles
Lesson Quiz: Part II
mXYZ = 2x° and mPQR = (8x - 20)°.
4. If XYZ and PQR are supplementary, find the
measure of each angle.
40°; 140°
5. If XYZ and PQR are complementary, find the
measure of each angle.
22°; 68°
Holt McDougal Geometry
1-4 Pairs of Angles
Warm Up
The measurement of angle XYZ = 2x° and
the measurement of angle
PQR = (8x – 20)°.
1.)If XYZ and PQR are supplementary find
the measure of each angle.
2.) If XYZ and PQR are complementary,
find the measure of each angle.
Holt McDougal Geometry