Standard G.G.13. Apply properties of angles, parallel lines, arcs, radii, chords, tangents, and secants to solve problems.

1.4: Measure and Classify Angles 1.5: Describe Angle Pair Relationships Objectives: By the end of this lesson I will be able to : 1.To define, classify, draw, name, and measure various angles 2.To use the Protractor and Angle Addition Postulates 3.To use special angle relationships to find angle measures

Angle angle sides vertexAn angle consists of two different rays (sides) that share a common endpoint (vertex). –Angle ABC,  ABC, or  B Sides Vertex A “Rabbit Ear” antenna is a physical model of an angle

Angle angle sides vertexAn angle consists of two different rays (sides) that share a common endpoint (vertex). –Angle ABC,  ABC, or  B

Example 1 How many angles can be seen in the diagram? Name all the angles. 3 <WXY <YXZ <WXZ

How Big is an Angle? Is the angle between the two hands of the wristwatch smaller than the angle between the hands of the large clock? –Both clocks read 9:36 Click me to learn more about measuring angles

Measure of an Angle measure of an angle The measure of an angle is the smallest amount of rotation about the vertex from one side to the other, measured in degrees. Can be any value between 0  and 180  Measured with a protractor

Classifying Angles

How To Use a Protractor The measure of this angle is written:

Example 2 Use the diagram to fine the measure of the indicated angle. Then classify the angle. 1.  KHJ 2.  GHK 3.  GHJ 4.  GHL = 55 = 125 = 180 = 90

Example 3. Use your protractor to measure the angles shown for exercises 3-5.

Example 4 What is the measure of  DOZ?

Example 4 Angle Addition Postulate You basically used the Angle Addition Postulate to get the measure of the angle, where m  DOG + m  GOZ = m  DOZ.

Angle Addition Postulate If P is in the interior of  RST, then m  RST = m  RSP + m  PST.

Example 5 Given that m  LKN = 145°, find m  LKM and m  MKN.

Congruent Angles congruent anglesTwo angles are congruent angles if they have the same measure. Add the appropriate markings to your picture.

Angle Bisector angle bisector An angle bisector is a ray that divides an angle into two congruent angles.

Example 6 In the diagram, YW bisects  XYZ, and m  XYW = 18°. Find m  XYZ.

Angle Pair Investigation In this Investigation, you will be shown examples and non-examples of various angle pairs. Use the pictures to come up with a definition of each angle pair.

Complementary Angles

Supplementary Angles

C Comes Before S…

Linear Pairs of Angles

linear pairTwo adjacent angles form a linear pair if their noncommon sides are opposite rays. supplementaryThe angles in a linear pair are supplementary.

Vertical Angles

vertical anglesTwo nonadjacent angles are vertical angles if their sides form two pairs of opposite rays. Vertical angles are formed by two intersecting lines.

Example 7 1.Given that  1 is a complement of  2 and m  1 = 68°, find m  2. 2.Given that  3 is a complement of  4 and m  3 = 56°, find m  4.

Example 8 Identify all of the linear pairs of angles and all of the vertical angles in the figure.

Example 9 Two angles form a linear pair. The measure of one angle is 5 times the measure of the other angle. Find the measure of each angle.