Angle Measure and Angle Addition

Angle Measure and Angle Addition

Ray

A ray is part of a line. It has one endpoint and extends infinitely in one direction. When you name a ray, the endpoint must be on the left.

Opposite Rays

Opposite rays are two rays with a common endpoint. The rays point in opposite directions.

Parts of an Angle

Types of Angles

Acute Angles

Acute angles measure between zero and 90 degrees.

Obtuse Angles

Obtuse angles measure between 90 and 180 degrees.

Right Angles

Right angles measure exactly 90 degrees.

Straight Angles

Straight angles measure exactly 180 degrees.

Congruent Angles

Congruent angles are angles that have the same measure.

Naming Angles

If Angles Share a Vertex

Angles can be named by 3 letters that define the angle with the vertex in the middle.

If Angles Have a Number in the Interior

Angles can be named by numbers found on the interior of the angle.

If Angles are Singular

If an angle is isolated, it can be named by its vertex.

Angle Addition

Angle Addition Postulate

Angle Bisector

Divides an angle into two equal parts.

Angle Addition Examples

Since ray FB bisects <AFC, m<1=m<2. Since ray FD bisects <CFE, m<3=m<4. Bisectors cut angles into 2 equal parts.

Congruent (equal) angles are designated with arc marks.

If m<3=67 and m<BFD=109, find m<2.

All you have to do is 109-67 and you get the m<2=42.

If m<2=48 and m<CFD=70, find m<BFD.

All you have to do is 48+70 and you get m<BFD=118.

If m<AFD=6x+4 and m<2=7x-2, find m<1.

All you have to do is solve

6x+4=7x-2. They are equal because the angles are congruent. Once you solve for x, plug it into 6x+4.

If m<3=6x+3 and m<4=8x-7, find m<DFE.

All you have to do is solve

6x+3=8x-7. They are equal because the angles are congruent. Once you solve for x, plug it into 8x-7.

If m<CFE=122 and m<1=5x+3, find x.

If m<1=5x+3, then m<2=5x+3 because they are congruent. All the angles add up to 180 because together they make a straight angle.

Multiple Choice

Blue outline is an example of...

• Angle

• Line

• Point

• Line segment

Multiple Select

Identify all of the ACUTE angles...

• 37^o

• 135^o

• 23^o

• 4^o

• 90^o

Multiple Choice

 $\overrightarrow{EJ}\$  bisects  $\angle DEF$ ,  $m\angle DEJ=5x+7$  ,  $m\angle JEF=8x-8$ .
Find x.

• 5

• 2

• 6

• 13

Multiple Choice

Angle JHG measures 161.

• m∠GHK=80.5,

  m∠KHJ=161

• m∠GHK=161,

  m∠KHJ=80.5

• m∠GHK=80.5,

  m∠KHJ=80.5

• m∠GHK=161,

  m∠KHJ=161

Multiple Choice

Find the value of ∠A.

• 25 degrees

• 30 degrees

• 35 degrees

• 90 degrees

Multiple Choice

• 50°

• 58°

• 115°

• 226°

Multiple Choice

• x = 6°

• x = 7°

• x = 12°

• x = 144°

Multiple Choice

Calculate m∠DEF.

• 180°

• 60°

• 120°

• 80°

Multiple Choice

Calculate m∠ABC.

• 45°

• 60°

• 105°

• 15°

Multiple Select

Select all of the ways you can name this angle.

• < ABC

• < B

• < C

• < 2

• < ACB

Multiple Choice

One way this angle can be named is:

• ∠ABC

• ∠ACB

• ∠BCA

• ∠CAB

Multiple Choice

The Vertex is which letter?

• A
• B
• C
• None of the above

Multiple Choice

Classify this angle.

• acute

• right

• obtuse

• none of the above

Multiple Choice

What is the measurement of a straight angle?

• 100
• 180
• 360
• 240

Multiple Choice

A part of a line that has one endpoint and goes on forever in the other direction

• Line
• Ray
• Line Segment
• Angle