1 Warm UP If m 1 23 º and m 2 32 º find the measures of all other angles Answers Adjacent Vertical Supplementary and Complementary Angles Adjacent angles are side by side and share a common ray ID: 908236
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Slide1
Lesson 1-5: Pairs of Angles
1
Warm UP: If m1 = 23 º and m2 = 32 º, find the measures of all other angles.
Answers:
Slide2Adjacent,
Vertical,
Supplementary, and Complementary Angles
Slide3Adjacent angles are “side by side” and share a common ray.
45
º
15
º
Slide4These are examples of adjacent angles.
55
º
35
º
50
º
130
º
80
º
45
º
85
º
20
º
Slide5These angles are NOT adjacent.
45
º
55
º
50
º
100
º
35
º
35
º
Slide6When 2 lines intersect, they make vertical angles.
75
º
75º
105º
105º
Slide7Vertical angles are opposite one another.
75
º
75
º
105
º
105
º
Slide8Vertical angles are opposite one another.
75
º
75
º
105
º
105
º
Slide9Vertical angles are congruent (equal).
30
º
150º
150
º30º
Slide10Supplementary angles add up to 180
º.
60º
120º
40
º
140
º
Adjacent and Supplementary Angles
Supplementary Angles
but not Adjacent
Slide11Complementary angles add up to 90
º.
60º30º
40
º
50
º
Adjacent and Complementary Angles
Complementary Angles
but not Adjacent
Slide12Practice Time!
Slide13Directions:
Identify each pair of angles as vertical, supplementary, complementary,
or none of the above.
Slide14#1
60
º
120º
Slide15#1
60
º
120º
Supplementary Angles
Slide16#2
60
º
30
º
Slide17#2
60
º
30
º
Complementary Angles
Slide18#3
75
º
75º
Slide19#3
75
º
75º
Vertical Angles
Slide20#4
60
º
40
º
Slide21#4
60
º
40
º
None of the above
Slide22#5
60
º
60º
Slide23#5
60
º
60º
Vertical Angles
Slide24#6
45
º
135º
Slide25#6
45
º
135º
Supplementary Angles
Slide26#7
65
º
25º
Slide27#7
65
º
25º
Complementary Angles
Slide28#8
50
º
90º
Slide29#8
50
º
90º
None of the above
Slide30Directions:
Determine the missing angle.
Slide31#1
45
º
?º
Slide32#1
45
º
135º
Slide33#2
65
º
?
º
Slide34#2
65
º
25
º
Slide35#3
35
º
?º
Slide36#3
35
º
35º
Slide37#4
50
º
?º
Slide38#4
50
º
130º
Slide39#5
140
º
?
º
Slide40#5
140
º
140
º
Slide41#6
40
º
?º
Slide42#6
40
º
50º
Slide43Sometimes the lines between Geometry and Algebra blur just a bit. For example, sometimes the missing angle is not just a letter but a problem to be solved. Let’s take a look.
We know that the two angles are supplementary…but how do we solve for X.
When we solve these types of problems we are going to have TWO ANSWERS…what does X equal and what is the measure of the missing angle.
FINDING THE MISSING ANGLE…WITH X.
Slide443) Solve for x.
3x°
2x°
FIND THE MISSING ANGLE AND X
What is the relationship? What do the two terms need to equal?
Slide457) Solve for x.
4x°
5x°
What is the relationship? What do the two terms need to equal?
FIND THE MISSING ANGLE AND X
Slide468) Solve for x.
2x + 10
3x + 20
(2x + 10) + (3x + 20) = 180 Combine Like Terms
5x + 30 = 180 Solve for X
5x = 150
x = 30
FIND THE MISSING ANGLE AND X
X = 30
3(30) + 20 = 110°
X = 30
2(30) + 10 = 70°
Slide474) Solve for x.
2x + 5
x + 25
FIND THE MISSING ANGLE AND X
What is the relationship? What do the two terms need to equal?
Slide48FIND THE MISSING ANGLE AND X