1. Angles

2. 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.

3. A B C ∠B ∠ 1 Notice that when you name an angle ∠ ABCwith three letters that the vertex letter is always in the middle. ∠ CBA 1 This angle can be named in four different ways.

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

5. View this clip about how to measure angles. Click here to view video

6.  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.

7. Measured in degrees Acute angleRight angleObtuse angle Straight angle

8.  The angle addition postulate states:  For any angle PQR, if A is in the interior of  ∠PQR, then m∠PQA + m∠AQR = ∠PQR P Q A R

9.  When working with angles, sometimes we compare angles.  These are adjacent angles – ones that share a vertex and a common side but no interior points.  Angle 1 and Angle 2 are said to be adjacent 1 2

10. 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 N O P

11. 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 A C B D W X YZ 25 55 125

12.  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

13.  Perpendicular lines are two intersecting straight lines that form right angles.  MN ⊥ OP, thus forming four right angles. M N O P