 Angles and Their Measures Unit 1 Day 4

Do Now  Match the angle with its classification Acute Right Obtuse Straight

Angles  Angle: two different ________ sharing a(n) ___________________  The rays are called the sides of the angle.  The initial point is called the vertex of the angle.

Naming Angles  We can name this angle _______, _______ or _______.  Ex. 1 Name the angles in the second figure.

Measuring Angles  The measure of angle A is denoted _____________.  We can measure angles with a _______________ using units called _______________.  Angles that have the same measure are called ______________________.  Angles are _____________  Angle measures are ____________ A B C

Protractor Postulate  The rays of an angle can be lined up with the real numbers from 0 to 180 (as though on a protractor).  The measure of an angle is equal to the absolute value of the difference between the real numbers corresponding to its two rays. A B C D

Interior vs. Exterior  A point is in the interior of an angle if ______________________________________  A point is in the exterior of an angle if _______________________________________

Angle Addition Postulate  If D is in the interior of  ABC, then m  ABD + m  DBC = _______

 Ex. 2 Given m  RQS = 62  and m  SQP = 18 , find m  RQP.  Ex. 3 Given m  PQS = 33  and m  RQP = 58 , find m  SQR.

 In this class (for now), we will restrict angle measurements to between 0  and 180 .  Acute:  Right:  Obtuse:  Straight:

Classifying Angles  Ex. 4 Classify the following angles   LMN   LMP   NMQ   LMQ

Adjacent Angles  Two angles are adjacent angles if they share a common vertex and side but have no common interior points.

Ex. 4: Drawing Adjacent Angles a) Draw two adjacent angles  RSP and  RST so that  RST is acute. b) …  RST is obtuse.

Closure   JKL is a straight angle, and m  JKM is 115º. H is a point in the interior of  JKM, and m  HKL is 130º. What is m  HKM?