Angles are another of the basics in geometry. You can use algebra to help measure angles*…much like you can with segments! In fact, it is all quite algebraic, really.
The most common unit for measuring an angle is the degree. There are 360º in a circle so 1º is 1/360 of a circle. A protractor is used to measure the degrees in an angle. A protractor can help you classify angles by their measure. When measuring with a protractor, you are measuring the opening of the angle or the interior of the angle. Types of Angles Angles are classified by their measures. The measure of an angle is the absolute value of the difference of the real numbers that the rays correspond to on a protractor. You can 'eyeball' the type of an angle quite easily. 

Acute Angle Measures greater than 0º and less than 90º 
Obtuse Angle Measures greater than 90º and less than 180º 
Straight Angle Formed by two opposite rays and measures 180º 

Right Angle Measures 90º 

Adjacent Angles two angles in the same plane with a common vertex and a common side but no common interior points 
Linear Angles a pair of adjacent angles whose noncommon sides share a common vertex and are opposite rays 
Complementary Angles two angles whose measures have a sum of 90º 
Supplementary Angles two angles whose measures have a sum of 180º 

Mr. Axton's room is adjacent to Ms. Skipper's room because they share a common wall. The wall in the picture is ray MO because this what makes the rooms adjacent. So, LMO is adjacent to OMN. 

The Angle Addition Postulate


Using the Angle Addition Postulate It's easy to find the measure of an angle. Here are some problems where you can use algebra to help you! C is in the interior of ABD. Find each of the following. Draw a picture to help you! a. mABD if mABC = 48º and mCBD = 85º b. mCBD if mABC = 32.9º and mABD = 53.5º Yikes! What to do? 

Step 1: Set up your problem. What information do you know? Let's start with problem a. You know that mABC = 48º. You also know that mCBD = 85º. You also know that mABC + mCBD = mABD. So, let's write this as a problem. 

ABD = ABC + CBD 

Step 2: Substitute numbers for the variables. Substitute what you know into your problem.


ABD = 48º + 85º 

Step 3: Simplify. Solve the problem. Voila! Easypeasy, lemonsqueasy! So, try the second one on your own. 

ABD = 48º + 85º ABD = 133º 

©2016 Sherry Skipper Spurgeon for Geometry Bugs Me All Rights Reserved 
