if we look around us, we will see angles everywhere. angles in daily life

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