Do Now Classify the following angles as obtuse, right, straight, or acute. 3. 1. 4. 2.

Chapter 1-Section 1 Angles SWBAT learn the basic terminology of angles and their degree measures. In addition students will be able to determine an angle in standard position with coterminal angles.

Basic Terms Two distinct points determine a line called line AB. Line segment AB—a portion of the line between A and B, including points A and B. Ray AB—portion of line AB that starts at A and continues through B, and on past B. A B A B A B

Basic Terms continued… Angle-formed by rotating a ray around its endpoint. The ray in its initial position is called the initial side of the angle. The ray in its location after the rotation is the terminal side of the angle. Vertex-the endpoint of the ray

Basic Terms continued… Positive angle: The rotation of the terminal side of an angle counterclockwise. Negative angle: The rotation of the terminal side is clockwise.

Naming an Angle An angle can be named using its vertex. (ONLY IF THERE IS ONE ANGLE OFF THAT VERTEX) Ex: angle C An angle also can be named using 3 letters with the vertex in the middle. Ex: angle ACB or angle BCA C . . A . B

Types of Angles The most common unit for measuring angles is the degree. 360° for a complete rotation of a ray. 1 ° = 1/360 of a rotation. θ is used to name an angle.

Complementary & Supplementary Angles Two positive angles whose sum is 90° are called complementary angles. Two positive angles whose sum is 180° are called supplementary angles.

Complementary Angles Find the measure of each angle. Since the two angles form a right angle, they are complementary angles. Thus, k  16 k +20 The two angles have measures of 43 + 20 = 63 and 43  16 = 27

Supplementary Angles Find the measure of each angle. Since the two angles form a straight angle, they are supplementary angles. Thus, 6x + 7 3x + 2 These angle measures are 6(19) + 7 = 121 and 3(19) + 2 = 59

Degree, Minutes, Seconds Portions of a degree are measured in minutes and seconds. One minute is 1/60 of a degree. One second is 1/60 of a minute. 12° 42’ 38” represents 12 degrees, 42 minutes, 38 seconds.  

Calculations Perform the calculation. Perform the calculation. Write Since 86 = 60 + 26, the sum is written Perform the calculation. Write  

Conversions Converting between decimal degrees and degrees, minutes & seconds.

Standard Position An angle is in standard position if its vertex is at the origin and its initial side is along the positive x-axis. Angles in standard position having their terminal sides along the x-axis or y-axis, such as angles with measures 90, 180, 270, and so on, are called quadrantal angles.

Coterminal Angles A complete rotation of a ray results in an angle measuring 360. By continuing the rotation, angles of measure larger than 360 can be produced. Such angles are called coterminal angles.

Coterminal Angles Find the angles of smallest possible positive measure coterminal with each angle. a) 1115 b) 187 Add or subtract 360 as may times as needed to obtain an angle with measure greater than 0 but less than 360. a) b) 187 + 360 = 173 1115 3(360 ) - o 35 =

Homework Page 6-7 #’s 10, 13, 14, 24, 26, 31, 37