1 4 Measuring Angles Think About it Angles

1. 4 Measuring Angles

Think About it…. Angles C, D, and E all appear to be the same size as the angle to the right. We could verify by measuring with a protractor or by moving the angle on top of the others to see if they line up correctly.

Angles Definitions Angle: formed by two rays with the same endpoint Rays: the sides of the angle Vertex: the point shared by both rays Diagram Sides Vertex A

Interior and Exterior Interior – region containing all of the points between the two sides of the angle Exterior – region containing all of the points outside of the angle Practice naming interior & exterior points, and points on the angle

Naming Angles You can name an angle by: Its vertex A point on each ray and the vertex (Vertex must be in middle) A number

You Try!

Measuring Angles Degrees – unit used for measuring angles Notation for measuring angles: m A = 62 “m” means “the measure of”

Protractor Postulate 125 m O = ____ Allows you to find the measure of an angle A protractor measure angles from 0º to 180º. Measuring with a protractor is only an estimate of the actual measure because there could be human error, and it doesn’t measure small enough (e. g. it cannot measure a 50. 7 angle, a 108. 456 angle, etc. )

Find the measure of COD. m COD = |45 – 147. 5| = 102. 5

Classifying Angles Acute Angle Right Angle Obtuse Angle Straight Angle

Examples:

Congruent Angles Congruent Anglesangles with the same measure Mark congruent angles with arcs to show they are congruent

You Try! If m KLM = 80 , and m ABC= 50 , find: 50 m DEF = _____ 80 m GHJ = _____

Angle Addition Postulate Part + Part = Whole

Example If m ADB = 36 , m BDC = 22 , find 58 m ADC = ____

Using the Angle Addition Postulate Q Plug it in!!!

You Try! 11 x – 12 + 2 x + 10 = 180 13 x – 2 = 180 13 x = 182 x = 14 m DEF = 11 x – 12 = 11(14) – 12 = 142 m CEF = 2 x + 10 = 2(14) + 10 = 38