Angle Relationships

Angle Relationships

Complementary and

Supplementary Angles

Today's Objective

Determine the measures of unknown angles using equations and angle relationships.

It's Time to Warm Up!

LINE

 $\overleftarrow{A}\overrightarrow{B}$  

LINE SEGMENT

 $\overline{AB}$  

RAY

 $\overrightarrow{AB}$  

ANGLE

 $\angle$ XYZ             m $\angle$  XYZ = $120\degree$  

 $\angle$ ZYX             m $\angle$  ZYX = $120\degree$  

 $\angle$ Y                  m $\angle$  Y = $120\degree$  

Rewind!

Lets rewind to class last week and review a few definitions.

Line  $\longleftrightarrow$  

series of points that extend in 2 opposite directions without end

Ray   $\longrightarrow$  
part of a line with 1 endpoint and points extending in 1 direction

Line Segment  $-$  
part of a line with 2 endpoints

Angle  $\angle$  
formed by 2 rays with a common endpoint (VERTEX)

How do we name the figures?

Line    $\overleftarrow{y}\overrightarrow{x}$  

Any two points on the line

Ray   $\overrightarrow{xy}$ 
Endpoint + any point on the ray

Line Segment  $\overline{xy}$ 
Starting point + end point

Angle    $\angle XYZ$    $\angle ZYX$   $\angle Y$  
Any point on one side + vertex + any point on the remaining side

Multiple Choice

Name the figure.

• Angle AB

• Line Segment AB

• Ray BA

• Line Segment BA

• Ray AB

Multiple Choice

Which term describes two rays with a common endpoint?

• Angle

• Ray

• Line segment

• Line

• Vertex

Multiple Select

What is the vertext of this angle?

• Point A

• Point B

• Point C

Multiple Select

This angle can be written as ______.

HINT: Select more than one answer.

• ∠ABC

• ∠ACB

• ∠CBA

• ∠CAB

• ∠B

Multiple Choice

Given angle  $\angle GHI$ , what's the vertex?

• G

• H

• I

• None

COMPLEMENTARY

ANGLES

Two angles are complementary if the sum (+) of the two angles = 90°.

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SUPPLEMENTARY

ANGLES

Two angles are supplementary if the sum (+) of the two angles = 180°.

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Multiple Choice

This picture shows

• an acute angle

• a parallel line

• a right angle

• two line segments

Multiple Choice

What is the measure of the missing angle?

• 39

• 129

• 119

• 129

Multiple Choice

Solve for x.

• x = 118

• x = 108

• x = 28

• x = 58

Multiple Choice

What is the value of "x"?

• 19

• 20

• 21

• 22

Multiple Choice

Find the value of x.

• 14

• 112

• 108

• 104

Notice and Wonder

Take 60 seconds to jot down

two things you notice and

one thing you wonder.

More Angle Relationships

Definitions:
Vertical angles are pairs of opposite angles that form when two lines meet at a point.
Congruent angles are angles that have the same measure.

Vertical angles:
  (1.) are congruent.
           $m\angle1\ \cong\ m\angle3$ 
           $m\angle4\ \cong\ m\angle2$    

 (2.) can be used to find the measure of supplemental angles.
           $m\angle1+m\angle2\ =\ 180\degree$ 
           $m\angle2+m\angle3\ =\ 180\degree$  

           $m\angle3+m\angle4\ =\ 180\degree$  
           $m\angle4+m\angle1\ =\ 180\degree$  

How can we solve for  $\angle1,\ \angle2,\ and\ \angle4?$  

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Multiple Choice

If m∠1 = 30°, then m∠3 =

• 30°

• 60°

• 150°

• undetermined

Multiple Choice

What is the measure of angle B?

• 100°

• 80°

• 90°

• 180°

Multiple Choice

What is the measure of angle A?

• 100°

• 80°

• 90°

• 180°

Problem Set 1

• 1. Use an equation to solve for x.

• 2. What is the measure of angle 1?

• 3. What is the measure of angle 2?

Problem Set 2

• 1. Find the measure of  $\angle AOC$ . 

• 2. Determine the measure of $\angle f$ .

• 3. Calculate the measure of  $\angle BOE$ . 

• 4. m $\angle EOC\ =$  ?

• 5. What is the total sum of  $\angle AOC,$    $\angle COE,\ \angle EOD,\ and\ \angle DOA$  ? 

• 6. Explain the relationship between the two pairs of vertical angles created by two interesecting lines (lines that meet at a point).

Today's Takeaways