Angles

Angles are formed by two rays that have a common endpoint.

A

B

C

Notice ray AB and ray BC have a common endpoint, point B.

Point B is called the vertex of the angle and ray BA and ray BC are called the sides.

A

B

C

∠B

∠ 1Notice that when you name an

angle ∠ ABC with three letters that the vertex

letter is always in the middle.∠ CBA

1

This angle can be named in four different ways.

Angles are measured in units called degrees. In order to measure angles, we use a tool called a protractor.

View this clip about how to measure angles.

Click here to view video

The Acute angle measures between 0 and 90 degrees.

The Right angle measures exactly 90 degrees.

The Obtuse angle measures between 90 and 180 degrees.

The Straight angle measures exactly 180.

Measured in degrees

P

Q

A

R

12

Linear Pair Angles

Linear Pair angles are adjacent angles that have their non-common side laying in a straight line.

∠ MNO and ∠ MNP are called linear pair angles.

M

NO P

Two angles that when added together equal 90 degrees. ∠ABC and ∠CBD are complementary angles.

Complementary angles

Two angles that when added together equal 180 degrees. ∠WYX and ∠ XYZ are supplementary angles.

Supplementary angles

AC

BD

W

X

Y Z

25

55 55125

Congruent angles are angles of equal measure. A special pair of angles that are congruent are the vertical angles.

∠1 and ∠3 are vertical angles and are equal in measure. ∠2 and ∠4 are vertical angles and are equal in measure.

1

2

3

4

Perpendicular lines are two intersecting straight lines that form right angles.

MN ⊥ OP, thus forming four right angles.

M

N

O P