Referent Angles Examples

Lesson 1: Angles - Referent Angle Examples

   Constructing Knowledge

When sketching approximate angles, it is not necessary to use a protractor. By knowing referent angles and using addition and subtraction, you can sketch most angles quite accurately.

The first step is always to use a ruler to draw a straight line (usually horizontal across the page). It is this horizontal line from which the angle is constructed. Referents (or a combination of referents) are used to form the approximate angle.

   Multimedia

A video describing referent angles is provided.

EXAMPLE 1

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Sketch the following angles without using a protractor.

1. 75°
2. 135°

Solution

1. The referent angles of 45° and 30° combined will add up to 75°.
   
   

   =		+
   =
   =



2. The referent angles of 90° and 45° combined will add up to 135°.
   
   

   		+
   =
   =

EXAMPLE 2

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Estimate the measure of the following angles

1. 
2. 

Solution

1. This angle is quite small. It can be compared to the referent angle of 22.5°.
   
   

   compared to

   
   
   From this comparison, it can be seen that the given angle is smaller than 22.5°. An appropriate estimate could be in the range of 15° to 20°.



2. This angle can be compared to a straight angle of 180°.
   
   

   compared to

   
   It looks like the given angle could be about 30° less than 180°.
   
   

   —

   
   An appropriate estimate could be 150°.

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