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If we look around us, we will see angles everywhere.
Angles In Daily Life
To name an angle, we name any point on one ray, then the vertex, and then any point on the other ray.
For example: ABC or CBA
We may also name this angle only by the single letter of the vertex, for example B.
A
BC
Naming An Angle
Adjacent angles are “side by side” and share a common ray.
45º15º
These are examples of adjacent angles.
55º
35º
50º130º
80º 45º
85º20º
These angles are NOT adjacent.
45º55º
50º100º
35º
35º
Complementary angles add up to 90º.
60º
30º40º
50º
Adjacent and Complementary Angles
Complementary Anglesbut not Adjacent
Complementary Anglessum to 90°
40°
50°
1) Find the missing angle.
36°
?°
Supplementary Anglessum to 180°
30° 150°
Supplementary angles add up to 180º.
60º120º
40º
140º
Adjacent and Supplementary Angles
Supplementary Anglesbut not Adjacent
6) Find the missing angle.
58° ?°
Two angles that have the same measure are called congruent angles.
Congruent angles have the same size and shape.
A
BC
300
D
EF
300
D
EF
300
Congruent Angles
Vertically Opposite AnglesVertically opposite angles are pairs of angles formed by two lines intersecting at a point.
APC = BPD
APB = CPD
A
DB
C
P
Four angles are formed at the point of intersection.
Point of intersection ‘P’ is the common vertex of the four angles.
Vertically opposite angles are congruent.
Vertical Anglesare opposite one another.
Vertical angles are congruent.
100°
100°
Vertical Anglesare opposite one another.
Vertical angles are congruent.
80°
80°
Name the vertically opposite angles and adjacent angles in the given figure:
A
DB
C
P
Vertically opposite angles: APC and BPD
APB and CPDAdjacent angles: APC and CPD
APB and BPD
Find the missing angles
Pairs Of Angles Formed by a Transversal
• Corresponding angles
• Alternate angles
• Interior angles
A line that intersects two or more lines at different points is
called a transversal.
Line L (transversal)
BALine M
Line NDC
P
Q
G
F
Pairs Of Angles Formed by a Transversal
Line M and line N are parallel lines.Line L intersects line M and line N at point P and Q.Four angles are formed at point P and another four at point
Q by the transversal L.Eight angles are formed in all by the transversal L.
Interior and exterior parts
Corresponding angles When two lines are crossed by the transversal the
angles in matching corners are called corresponding angles.
Corresponding angles
You need a pair of parallel lines.
Draw any line to cut the pair of parallel lines.
What angle is the same as the red one?
correspondingangles
How do you tell angles are corresponding?
Look for a letter F in any orientation.
correspondingangles
Alternate interior angles
• Alternate Interior angles are two nonadjacent interior angles that lie on opposite sides of a transversal.
Alternate Exterior angles
Alternate Exterior angles are the angle pairs that are on the outsides of the two lines (the exterior) and on opposite (or alternate sides) of the transversal.
Alternate interior angles
Alternateinterior angles
You need a pair of parallel lines.
Draw any line to cut the pair of parallel lines.
What angle is the same as the blue one?
How do you tell angles are alternate interior ?
Look for a letter Z in any orientation.
Alternateinterior angles
Name the pair of alternate interior and exterior angles?
Practice Time!
2.
1.
3. 4.
5. 6.7. 8.
Angle 2 measures 110°. What do the other angles measure?
1) Find the missing angle.
36°
?°
1) Find the missing angle.
36°
?°
1) Find the missing angle.
36°
?°
90 ° – 36 = 54°
2) Find the missing angle.
64°
?°
2) Find the missing angle.
64°
?°
90 ° – 64° = 26°
3) Solve for x.
3x°
2x°
3) Solve for x.
3x°
2x°
3x° + 2x° = 90°
5x = 90
x =18
4) Solve for x.
2x + 5
x + 25
4) Solve for x.
2x + 5
x + 25
(2x + 5) + (x + 25) = 90
3x + 30 = 90
3x = 60
x = 20
5) Find the missing angle.
?° 168°
5) Find the missing angle.
?° 168°
180° – 168° = 12°
6) Find the missing angle.
58° ?°
180° – 58° = 122°
7) Solve for x.
4x 5x
7) Solve for x.
4x 5x
4x + 5x = 180
9x = 180
x = 20
8) Solve for x.
2x + 10 3x + 20
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