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All about Angles!

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.

*an angle is the figure formed by two rays with a common endpoint called the vertex. The interior of the angle is the set of all the points between the sides of the angle and the exterior of the angle is the set of all points outside the angle.

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 18

Straight Angle

Formed by two opposite rays and measures 18

Right Angle

Measures 90º

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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 non-common 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, anglesymbol6LMO is adjacent to anglesymbol6a OMN.


The Angle Addition Postulate

If C is in the interior of anglesymbolABC, then manglesymbol1ABC + manglesymbol1aCBD = manglesymbol1b ABD

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 anglesymbol2 ABD. Find each of the following. Draw a picture to help you!

a. manglesymbol3ABD if manglesymbol4ABC = 48º and manglesymbol5CBD = 85º

b. manglesymbol3aCBD if manglesymbol4aABC = 32.9º and manglesymbol5aABD = 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 manglesymbol4bABC = 48º.

You also know that manglesymbol5bCBD = 85º.

You also know that manglesymbol4b1ABC + manglesymbol5b1CBD = manglesymbol5b2ABD.

So, let's write this as a problem.

anglesymbol5b2aABD = anglesymbol5b2bABC + anglesymbol5b2cCBD

Step 2: Substitute numbers for the variables.

Substitute what you know into your problem.

manglesymbol4b2ABC = 48º
manglesymbol5b3CBD = 85º

anglesymbol5b2a1ABD = 48º + 85º

Step 3: Simplify.

Solve the problem.

Voila! Easy-peasy, lemon-squeasy!

So, try the second one on your own.

anglesymbol5b2a1aABD = 48º + 85º

anglesymbol5b2a1a1ABD = 133º

©2016 Sherry Skipper Spurgeon for Geometry Bugs Me

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