Angle relationships
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Transcript of Angle relationships
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Angle Relationships&
Parallel LinesPre-Algebra
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Adjacent angles are “side by side” and share a common ray.
45º15º
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These are examples of adjacent angles.
55º
35º
50º130º
80º 45º
85º20º
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These angles are NOT adjacent.
45º55º
50º100º
35º
35º
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Complementary Anglessum to 90°
40°
50°
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Complementary angles add up to 90º.
60º
30º40º
50º
Adjacent and Complementary Angles
Complementary Anglesbut not Adjacent
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Supplementary Anglessum to 180°
30° 150°
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Supplementary angles add up to 180º.
60º120º
40º
140º
Adjacent and Supplementary Angles
Supplementary Anglesbut not Adjacent
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Vertical Anglesare opposite one another.
Vertical angles are congruent.
100°
100°
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Vertical Anglesare opposite one another.
Vertical angles are congruent.
80°
80°
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Lines l and m are parallel.l||m
120°
l
m
120°
120°
120°
Note the 4 angles that measure 120°.
nLine n is a transversal.
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Lines l and m are parallel.l||m
60°
l
m
60°
60°
60°
Note the 4 angles that measure 60°.
nLine n is a transversal.
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Lines l and m are parallel.l||m
60°
l
m
60°
60°
60°
There are many pairs of angles that are supplementary.
There are 4 pairs of angles that are vertical.
120°
120°
120°
120°
nLine n is a transversal.
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If two lines are intersected by a transversal and any of the angle pairs shown below are congruent, then the lines are parallel. This fact is used in the construction of parallel lines.
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Practice Time!
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1) Find the missing angle.
36°
?°
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1) Find the missing angle.
36°
?°
90 ° – 36 = 54°
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2) Find the missing angle.
64°
?°
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2) Find the missing angle.
64°
?°
90 ° – 64° = 26°
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3) Solve for x.
3x°
2x°
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3) Solve for x.
3x°
2x°
3x° + 2x° = 90°
5x = 90
x =18
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4) Solve for x.
2x + 5
x + 25
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4) Solve for x.
2x + 5
x + 25
(2x + 5) + (x + 25) = 90
3x + 30 = 90
3x = 60
x = 20
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5) Find the missing angle.
?° 168°
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5) Find the missing angle.
?° 168°
180° – 168° = 12°
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6) Find the missing angle.
58° ?°
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6) Find the missing angle.
58° ?°
180° – 58° = 122°
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7) Solve for x.
4x 5x
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7) Solve for x.
4x 5x
4x + 5x = 180
9x = 180
x = 20
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8) Solve for x.
2x + 10 3x + 20
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8) Solve for x.
2x + 10 3x + 20
(2x + 10) + (3x + 20) = 180
5x + 30 = 180
5x = 150
x = 30
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9) Lines l and m are parallel.l||m
Find the missing angles.
42°
l
m
b°
d°
f°
a °
c°
e°
g°
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9) Lines l and m are parallel.l||m
Find the missing angles.
42°
l
m
42°
42°
42°
138°
138°
138°
138°
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10) Lines l and m are parallel.l||m
Find the missing angles.
81°
l
m
b°
d°
f°
a °
c°
e°
g°
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10) Lines l and m are parallel.l||m
Find the missing angles.
81°
l
m
81°
81°
81°
99°
99°
99°
99°
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11) Find the missing angles.
70 °b°
70 °
d ° 65 °
Hint: The 3 angles in a triangle sum to 180°.
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11) Find the missing angles.
70 °40°
70 °
75 ° 65 °
Hint: The 3 angles in a triangle sum to 180°.
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12) Find the missing angles.
45 °b°
50 °
d ° 75 °
Hint: The 3 angles in a triangle sum to 180°.
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12) Find the missing angles.
45 °85°
50 °
20° 75 °
Hint: The 3 angles in a triangle sum to 180°.
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In the figure a || b.
13. Name the angles congruent to ∠3.
14. Name all the angles supplementary to ∠6.
15. If m∠1 = 105° what is m∠3?
16. If m∠5 = 120° what is m∠2?
∠1, ∠5, ∠7
∠1, ∠3, ∠5, ∠7
105°
60°
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The End