1-4: Measuring Angles

Parts of an Angle

• An angle is formed by two rays with the same endpoint.

• The rays are the sides of the angle and the endpoint is the vertex of the angle.

• The interior of an angle is the region containing all points between the sides of the angle.

• The exterior of an angle is the region containing all points outside the angle.

Naming an Angle

• You can name an angle by its vertex (A), a point on each ray and the vertex (BAC or CAB), or a number (1).

*Note: When using 3 points to name an angle, the vertex must go in the middle!

Naming Angles

• What are two other names for 1?

• What are two other names for KML?

Measuring Angles

• One way to measure the size of an angle is in degrees.

• To say that the measure of A is 62, you would write mA = 62.

Protractor Postulate: Consider OB and point A on one side of OB. Every ray of the form OA can be paired one to one with a real number from 0 to 180.

Types of Angles

• You can classify angles according to their measures.

Symbol for right angle!

Measuring and Classifying Angles

• What are the measures of LKN, JKL, and JKN?

• Classify each as acute, right, obtuse, or straight.

Congruent Angles

• Angles with the same measure are congruent angles.

• This means that if mA = mB, then A B (and vice versa).

• You can mark angles with arcs to show they are congruent.

Using Congruent Angles

• Synchronized swimmers form angles with their bodies.

• If mGHJ = 90, what is mKLM?

• If mABC = 49, what is mDEF?

Which angle is congruent to WBM?

Angle Addition

Angle Addition Postulate: If point B is in the interior of AOC, then mAOB + mBOC = mAOC.

Using the Angle Addition Postulate

• If mRQT = 155, what are mRQS and mTQS?

If mABC = 175, what are mABD and mCBD?