holt mcdougal geometry 1-4 pairs of angles simplify each expression. 1. 90 – (x + 20) 2. 180 –...
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Holt McDougal Geometry
1-4 Pairs of Angles
Simplify each expression.
1. 90 – (x + 20)
2. 180 – (3x – 10)
Write an algebraic expression for each of the following.
3. 4 more than twice a number
4. 6 less than half a number
70 – x
190 – 3x
2n + 4
Flashback
Holt McDougal Geometry
1-4 Pairs of Angles
Identify adjacent, vertical, complementary, and supplementary angles.
Find measures of pairs of angles.
GOALS!
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
Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.
Example 1: Identifying Angle Pairs
AEB and BED
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.
Example 2: Identifying Angle Pairs
AEB and BEC
Only adjacent
Holt McDougal Geometry
1-4 Pairs of Angles
DEC and AEB
Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.
Example 3: Identifying Angle Pairs
Not Adjacent
Holt McDougal Geometry
1-4 Pairs of Angles
5 and 6
Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.
Adjacent and form a linear pair
Check Up
Holt McDougal Geometry
1-4 Pairs of Angles
7 and SPU
Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.
Not adjacent
Check Up
Holt McDougal Geometry
1-4 Pairs of Angles
7 and 8
Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.
Not adjacent
Check Up
Holt McDougal Geometry
1-4 Pairs of Angles
Complementary angles-
What is the complement of 30⁰?
What is the complement of 44.2⁰?
Holt McDougal Geometry
1-4 Pairs of Angles
Complementary angles-
What 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 angles-
What 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
Find the measure of each of the following.
Example 4: Finding the Measures of Complements and Supplements
A. complement of F
B. supplement of G
90 – 59 = 31
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
(90 – x)
Holt McDougal Geometry
1-4 Pairs of Angles
a. complement of E
Find the measure of each of the following.
b. supplement of F
= (102 – 7x)°
180 – 116.5° =
90° – (7x – 12)° = 90° – 7x° + 12°
(90 – x)°
(180 – x)
Check Up
Holt McDougal Geometry
1-4 Pairs of Angles
Find the measure of each of the following.
Example 3: Using complements and supplements
A. Find the value of b.
B. Find the value of x
b = 27
93 + 3x + 18 = 180
X = 23
63 + b = 90
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
x = 14
Set up the equation!
Solve for x!
R = 49 and 41
Holt McDougal Geometry
1-4 Pairs of AnglesCheck Up
∠DEF and ∠FEG are supplementary. m∠DEF = 9x + 1 and m∠FEG = 8x + 9. Find the measure of both angles.
x = 10 ∠DEF = 91 and ∠FEG =89
Holt McDougal Geometry
1-4 Pairs of Angles
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 m1 = 47°, find m2, m3, and m4.
Example 7: Problem-Solving Application
m2 = 47°, m3 = 43°, and m4 =43°.
Holt McDougal Geometry
1-4 Pairs of Angles
What if...? Suppose m3 = 27.6°. Find m1, m2, and m4.
Check Up
Thus m1 = m2 = 62.4°; m4 = 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
Need: straightedge and protractor
Draw large X.
Number the angles 1, 2,3,4
Measure all four angles
What is the result?
Look through the basic terms, what type of angles are these?
Holt McDougal Geometry
1-4 Pairs of Angles
Vertical angles
A and C are vertical angles, as are B and D.
Name two sets of vertical angles
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
mA = 64.1°, and mB =(4x – 30)°. Find the measure of each of the following.
1. supplement of A
2. complement of B
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°.
(120 – 4x) °
115.9°
False; each is 45°.
Holt McDougal Geometry
1-4 Pairs of Angles
Lesson Quiz: Part II
mXYZ = 2x° and mPQR = (8x - 20)°.
4. If XYZ and PQR are supplementary, find the measure of each angle.
5. If XYZ and PQR are complementary, find the measure of each angle.
22°; 68°
40°; 140°
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.