Lesson 11

Special Angles

Different types of Angles

• There are some special types of angles that you need to know.

• Supplementary- Two angles are supplementary when the sum of their measures is 180°. They form a straight line.

• Can you think of any more combinations of supplementary angles?

57° 123°

Another angle

• Complementary- Two angles are complementary if the sum of their measures is 90°. They create a right angle.

• Can you think of any more combinations of complementary angles?

55° 35°

What is the measure?

What is the measure of the missing angle?

What kind of angle are we dealing with?

What information do we know?

What should we do?

10°?°

More angles

• Vertical angles- are congruent angles. This means they have equal measures. They are pars of opposite angles formed when two lines (segments) intersect.

These are equal.

These are equal.

And these are equal.

And these are equal.

Another example

• Lines PQ and RS below intersect at point T. What is the measure of <RTQ?

55°

125°

P

R

T

Q

S

Next one

• Angle bisector- a ray, line segment or line that divides an angle into two congruent angles.

• Perpendicular bisector- a line, line segment or ray that is both perpendicular to the segment and bisects the segment. It creates right angles at the point of intersection.

Examples

C B

A

D

Ray BD is an angle bisector.

P

X

R

HG

Line PR is a perpendicular bisector.

Example

• Line segment AB is a perpendicular bisector of FG , intersecting FG at point B. Ray BQ is an angle bisector of <FBA. What is the measure of <FBQ?

F B G

AQ

Some examples

• Which of the following could be the measures of 2 supplementary angles?

a.30° and 50°

b.30° and 60°

c.70° and 100°

d.70° and 110°

Problem #2

• What is the measure of <STV below?

WT

S V

72°

Problem #3

• Line RS and TV intersect to form angles 1,2,3 and 4. Which statement about the measures of these angles is NOT true?

• Angles 1 and 3 have equal measures.• Angles 2 and 4 have equal measures.• Angle 1 is supplementary to angle 3• Angle 1 is supplementary to angle 4.

R

T S

V

43

21

Lets take a look

• Someone please read for me problem #4 on page 73

Homework

• Complete page 75-76