Angle Pairs (Complementary, Supplementary, Adjacent, Vertical, Linear Pair)
Chapter 1 Section 1.5 Angle Pair Relationships Linear Pair Two adjacent angles form a linear pair if...
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Transcript of Chapter 1 Section 1.5 Angle Pair Relationships Linear Pair Two adjacent angles form a linear pair if...
![Page 1: Chapter 1 Section 1.5 Angle Pair Relationships Linear Pair Two adjacent angles form a linear pair if their noncommon sides are opposite rays. –Form a.](https://reader036.fdocuments.net/reader036/viewer/2022081506/56649ec05503460f94bcbf0b/html5/thumbnails/1.jpg)
Chapter 1Section 1.5
Angle Pair Relationships
![Page 2: Chapter 1 Section 1.5 Angle Pair Relationships Linear Pair Two adjacent angles form a linear pair if their noncommon sides are opposite rays. –Form a.](https://reader036.fdocuments.net/reader036/viewer/2022081506/56649ec05503460f94bcbf0b/html5/thumbnails/2.jpg)
Linear Pair
• Two adjacent angles form a linear pair if their noncommon sides are opposite rays.– Form a straight angle.
• Any two angles that form a linear pair have a sum of 180°.
1 and 2 form a linear pair
m1 + m2 =180°
1 2
![Page 3: Chapter 1 Section 1.5 Angle Pair Relationships Linear Pair Two adjacent angles form a linear pair if their noncommon sides are opposite rays. –Form a.](https://reader036.fdocuments.net/reader036/viewer/2022081506/56649ec05503460f94bcbf0b/html5/thumbnails/3.jpg)
Vertical Angles
• Two angles are vertical if their sides form two pairs of opposite rays.
• Vertical Angles are congruent
12
34
1 and 3 are vertical angles
4 and 2 are vertical angles
![Page 4: Chapter 1 Section 1.5 Angle Pair Relationships Linear Pair Two adjacent angles form a linear pair if their noncommon sides are opposite rays. –Form a.](https://reader036.fdocuments.net/reader036/viewer/2022081506/56649ec05503460f94bcbf0b/html5/thumbnails/4.jpg)
Use the figure to answer the questions
1. Are 1 and 2 a linear pair?
• Yes
2. Are 4 and 5 a linear pair?
• No
3. Are 3 and 1 vertical angles?
• No
4. Are 2 and 5 vertical angles?
• Yes
![Page 5: Chapter 1 Section 1.5 Angle Pair Relationships Linear Pair Two adjacent angles form a linear pair if their noncommon sides are opposite rays. –Form a.](https://reader036.fdocuments.net/reader036/viewer/2022081506/56649ec05503460f94bcbf0b/html5/thumbnails/5.jpg)
Use the figure to answer the questions
5. If m6 = 51°, then m7 = _____
• 129° -- Linear Pair
6. If m8 = 103°, then m6 =_____
• 103° -- Vertical Angels
7. If m9 = 136°, then m8 =_____
5. 44° -- Linear Pair
• If m7 = 53°, then m9 =_____
5. 53° -- Vertical Angles
![Page 6: Chapter 1 Section 1.5 Angle Pair Relationships Linear Pair Two adjacent angles form a linear pair if their noncommon sides are opposite rays. –Form a.](https://reader036.fdocuments.net/reader036/viewer/2022081506/56649ec05503460f94bcbf0b/html5/thumbnails/6.jpg)
Complementary Angles
• Two angles are complementary if their sum is 90°.
• Each Angle is the complement of the other
mA + mB = 90 °
A and B are complementary
30°
60°
A
B
![Page 7: Chapter 1 Section 1.5 Angle Pair Relationships Linear Pair Two adjacent angles form a linear pair if their noncommon sides are opposite rays. –Form a.](https://reader036.fdocuments.net/reader036/viewer/2022081506/56649ec05503460f94bcbf0b/html5/thumbnails/7.jpg)
Supplementary Angles
• Two angles are supplementary if their sum is 180°.
• Each angle is the supplement of the other
mA + mB = 180 °
A and B are complementary
120°60°
A
B
![Page 8: Chapter 1 Section 1.5 Angle Pair Relationships Linear Pair Two adjacent angles form a linear pair if their noncommon sides are opposite rays. –Form a.](https://reader036.fdocuments.net/reader036/viewer/2022081506/56649ec05503460f94bcbf0b/html5/thumbnails/8.jpg)
A and B are complementary and B and C are supplementary
9. If mA = 48° then mB = _____ and mC = _____
• mA + mB = 90°
• 48° + mB = 90°
• mB = 42°
• mB + mC = 180°
• 42° + mC = 180°
• mC = 138°
![Page 9: Chapter 1 Section 1.5 Angle Pair Relationships Linear Pair Two adjacent angles form a linear pair if their noncommon sides are opposite rays. –Form a.](https://reader036.fdocuments.net/reader036/viewer/2022081506/56649ec05503460f94bcbf0b/html5/thumbnails/9.jpg)
A and B are complementary and B and C are supplementary
10. If mB = 83° then mA = _____ and mC = _____
• mA + mB = 90°
• mA + 83° = 90°
• mA = 7°
• mB + mC = 180°
• 83° + mC = 180°
• mC = 97°
![Page 10: Chapter 1 Section 1.5 Angle Pair Relationships Linear Pair Two adjacent angles form a linear pair if their noncommon sides are opposite rays. –Form a.](https://reader036.fdocuments.net/reader036/viewer/2022081506/56649ec05503460f94bcbf0b/html5/thumbnails/10.jpg)
A and B are complementary and B and C are supplementary
11. If mC = 127° then mB = _____ and mA = _____
• mC + mB = 180°
• 127° + mB = 180°
• mB = 53°
• mA + mB = 90°
• mA + 53° = 90°
• mA = 37°
![Page 11: Chapter 1 Section 1.5 Angle Pair Relationships Linear Pair Two adjacent angles form a linear pair if their noncommon sides are opposite rays. –Form a.](https://reader036.fdocuments.net/reader036/viewer/2022081506/56649ec05503460f94bcbf0b/html5/thumbnails/11.jpg)
A and B are complementary and B and C are supplementary
12. If mA = 25° then mB = _____ and mC = _____
• mA + mB = 90°
• 25° + mB = 90°
• mB = 65°
• mB + mC = 180°
•65° + mC = 180°
• mC = 115°
![Page 12: Chapter 1 Section 1.5 Angle Pair Relationships Linear Pair Two adjacent angles form a linear pair if their noncommon sides are opposite rays. –Form a.](https://reader036.fdocuments.net/reader036/viewer/2022081506/56649ec05503460f94bcbf0b/html5/thumbnails/12.jpg)
Find the value of the variable
Vertical Angles are congruent
Solve for y
y + 20° = 70°
y = 50°
Solve for x
2x + 40 = 110
2x = 70
x = 35°
![Page 13: Chapter 1 Section 1.5 Angle Pair Relationships Linear Pair Two adjacent angles form a linear pair if their noncommon sides are opposite rays. –Form a.](https://reader036.fdocuments.net/reader036/viewer/2022081506/56649ec05503460f94bcbf0b/html5/thumbnails/13.jpg)
Find the value of the variable
Linear Pairs are add up to 180°
x + 168° = 180°
x = 12°
Vertical Angles are congruent
y = 168°
![Page 14: Chapter 1 Section 1.5 Angle Pair Relationships Linear Pair Two adjacent angles form a linear pair if their noncommon sides are opposite rays. –Form a.](https://reader036.fdocuments.net/reader036/viewer/2022081506/56649ec05503460f94bcbf0b/html5/thumbnails/14.jpg)
Find the value of the variable
Solve for x
48 + x = 64
x = 16
Vertical Angles are congruent
Solve for y
8y + 36 = 14y – 24
36 = 6y – 24
60 = 6y
10 = y
![Page 15: Chapter 1 Section 1.5 Angle Pair Relationships Linear Pair Two adjacent angles form a linear pair if their noncommon sides are opposite rays. –Form a.](https://reader036.fdocuments.net/reader036/viewer/2022081506/56649ec05503460f94bcbf0b/html5/thumbnails/15.jpg)
![Page 16: Chapter 1 Section 1.5 Angle Pair Relationships Linear Pair Two adjacent angles form a linear pair if their noncommon sides are opposite rays. –Form a.](https://reader036.fdocuments.net/reader036/viewer/2022081506/56649ec05503460f94bcbf0b/html5/thumbnails/16.jpg)
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Homework #6 Pg 38: 1-7, 9-15
odd, 16, 17-27 odd, 28-35, 46-54, 57,61