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Using a Protractor

Date: 06/28/98 at 14:51:10
Subject: Intersecting parallel lines

I need to know how to find angles and to use a protractor. 

I made two parallel lines - now I have to intersect those lines making 
a 65-degree angle. Help!

Date: 06/29/98 at 17:07:24
From: Doctor Peterson
Subject: Re: Intersecting parallel lines

Hi, Michelle. Protractors can be a little confusing. Let's take out 
your protractor and look closely at it. Mine is not very round after 
passing through e-mail, but you should more or less recognize it:

                            90            /
                        _ - -+- - _      /
                     /      9|0      \  /D
                 /           |         / \
           135 /             |        /    \  45
             / 45            |       /   135 \
           /                 |      /          \
          /                  |     /            \
         /                   |    /              \
        /                    |   /                \
        /                    |  /                 \
        |                    | /                  |
        |                    |/                   |
        A                   /C                    B

What you should see on yours (and on mine if I could draw it better!) 

   - a line along the bottom (AB), which you have to line up with the      
     line you want to make a 65 degree angle with;

   - a cross or dot in the middle of that line (C), which marks the 
     center of the angle you are going to measure (so you should first 
     make a small mark there to show the point your line will go 

   - a semicircle around the edge, with little degree marks;

   - degree labels around the outside, probably going in both 
     directions (clockwise and counterclockwise) from 0 to 180.

To draw a line at a 65-degree angle, facing to the right, look for the 
numbers that start at 0 on the right (that's the outside set of 
numbers on mine) and look along them until you come to 60 and 70. Just 
as on a ruler, there should be some number of divisions between them, 
and you should be able to identify a mark for 65 degrees halfway 
between 60 and 70.

Make a small mark there (D), and then remove the protractor. Now you 
can use your ruler to draw a line between the marks (CD), and you're 

If you have to measure an angle you've been given - maybe where the 
line you just drew meets the other parallel line - then you do the 
same thing in reverse. You line up the bottom edge with one of the 
lines that make the angle, with the center mark (C) over the place 
where the lines meet. Then you find which set of numbers starts at 
zero on the first line, and follow it until you come to the second 
line. Then you read the numbers just like a ruler.

Have fun drawing and measuring, and let us know if you need more help, 
or if you discover any great theorems while you explore!

- Doctor Peterson, The Math Forum   

Date: 04/04/2001 at 10:25:40
From: chad
Subject: Using a protractor

How do you use a protractor to find the three angle measures of a 
triangle ?

Date: 04/04/2001 at 12:14:40
From: Doctor Peterson
Subject: Re: Using a protractor

I'll give you a few additional pointers for measuring a triangle.

First, if the triangle is smaller than your protractor, you will have to 
extend the edges, like this, so they are long enough to reach the edge of 
the protractor:

         \     /
           \  /
            /  \
           /     \
         /           \
        /              \

Now put the center of the protractor on one of the vertices, and line up 
the zero on one of the two curved scales with one of the edges coming from 
that vertex. Follow along that scale (watching the numbers increase from 
zero) until you come to the other edge (ray) of that angle. The number you 
find there is the measure of the angle. 

You may have to count small marks to decide how many degrees each mark 
indicates. For instance, if the scale looks like

          |                   |
         70                  80

then since there are five spaces between 70 and 80, each is 2 degrees 
(1/5 of 10 degrees), and the mark I am measuring is at about 77 degrees.

- Doctor Peterson, The Math Forum   

Associated Topics:
Elementary Geometry
Elementary Triangles and Other Polygons
Elementary Two-Dimensional Geometry
Middle School Geometry
Middle School Triangles and Other Polygons
Middle School Two-Dimensional Geometry

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