simplify each expression. 1. 90 – ( x + 20) 2. 180 – (3 x – 10)
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Flashback. Simplify each expression. 1. 90 – ( x + 20) 2. 180 – (3 x – 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 – 3 x. 2 n + 4. GOALS!. - PowerPoint PPT PresentationTRANSCRIPT
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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
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Holt McDougal Geometry
1-4 Pairs of Angles
Identify adjacent, vertical, complementary, and supplementary angles.
Find measures of pairs of angles.
GOALS!
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Holt McDougal Geometry
1-4 Pairs of Angles
Draw an example of adjacent angles.
Draw an example of a linear pair.
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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
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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
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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
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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
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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
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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
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Holt McDougal Geometry
1-4 Pairs of Angles
Complementary angles-
What is the complement of 30⁰?
What is the complement of 44.2⁰?
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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
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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
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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°.
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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)
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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
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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
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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
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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
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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°.
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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°.
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Holt McDougal Geometry
1-4 Pairs of Angles
Assignment: Page 32 14-21,26-31
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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.
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Holt McDougal Geometry
1-4 Pairs of Angles
Day 2 Vertical Angles
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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?
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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?
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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°.
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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°
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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.