1-4: Measuring Angles
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?