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Measuring Angles with a Protractor

Date: 02/28/2002 at 07:12:14
From: Rezzi
Subject: Angles

I want to know how to measure acute, reflex and obtuse angles with a 

Date: 02/28/2002 at 09:53:33
From: Doctor Rick
Subject: Re: Angles

Hi, Rezzi.

To measure an acute angle (less than 90 degrees), put the vertex at 
the center of the straight side of the protractor, lining up one half 
of that side with one side of the angle, so that the other side is 
under the protractor. On the curved edge of the protractor are 
(usually) two sets of numbers; one scale starts with zero on the left 
edge and increases to the right, while the other starts with zero on 
the right edge and increases to the left. Choose the scale that starts 
on the side that you lined up with a side of the angle. Read off the 
number from this scale at the point where the other side of the angle 
crosses the protractor.


Measuring obtuse angles (between 90 and 180 degrees) works exactly the 
same way. It may be that some protractors have only one scale, with 
zero on both ends and 90 in the middle. If so, then you'll read a 
number between 0 and 90, and you'll need to subtract it from 180 to 
get the measure of the obtuse angle. For instance, if you read 45, the 
angle is really 

  180 - 45 = 135 degrees

A reflex angle is the "outside" of an acute or obtuse angle. Use the 
protractor to read the measure of the "inside" of the angle. Then 
subtract from 360 to get the measure of the reflex angle. If the 
inside is the same obtuse angle we just measured, then the measure of 
the outside is

  360 = 135 = 225 degrees

Does that help?

- Doctor Rick, The Math Forum   

Date: 07/14/2003 at 16:35:03
From: Gloria 
Subject: Reading the measurements on the protractor

I have different pictures of a protractor with arrows pointing to 
different numbers on it. None of them starts at 0. This protractor is 
0-180. If I have arrows pointing to 80-150, do I start at 0? Or would 
I just say 70 and subtract from 180? I'm confused!

Date: 07/14/2003 at 17:05:39
From: Doctor Peterson
Subject: Re: Reading the measurements on the protractor

Hi, Gloria.

I think you mean that you are supposed to find the angle between the 
80 and 150 marks on the protractor. Although you would normally set 
the protractor so that one leg of the angle lies at zero, you can 
also use it this way. Remember that a protractor is really just a 
curved ruler, and can be used in exactly the same ways (apart from 
having to put the vertex of the angle in the right place). On a 
ruler, you can measure starting at zero:

  0   1   2   3   4   5   6   7   8
        5 inches

or between any two positions:

  0   1   2   3   4   5   6   7   8
              7-2=5 inches

You subtract the readings of the two ends to find the distance between 

So the angle between the 80 and 150 marks is just 150-80 = 70 degrees. 
What you are really doing is subtracting two angles. If the points at 
the 0, 80, and 150 degree marks are P, Q, and R, and the center of the 
protractor is at O, then you are measuring angles QOR as POR - POQ. 
Draw a picture of that and see if it makes sense.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
Associated Topics:
High School Euclidean/Plane Geometry
High School Geometry
Middle School Geometry
Middle School Measurement
Middle School Two-Dimensional Geometry

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