How to Construct a 45 Degrees Angle Using Compass and Straightedge

This article teaches you how to construct a 45^o angle using a compass and a straightedge by different methods.

Edit Steps

Edit Method One: Starting with the Vertex

1. Mark the vertex of your angle anywhere on the paper. Let us name this point as M.
   
   
   
   
   
   
   


2. Draw a ray MN, extending in any direction and of any length. This will be one of the arms of our angle.
   
   
   
   
   
   
   


3. Drop a perpendicular to the ray MN at any randomly chosen point (say X) on it.
   
   
   
   
   
   
   


4. Set width of your compass equal to the distance MX. Retain this width for the following step.
   
   
   
   
   
   
   


5. Place tip of the compass on X and draw an arc so as to cut the perpendicular at some point (say Y).
   
   
   
   
   
   
   


6. Connect the points M and Y with a straight line and extend it to form a ray ML.
   
   
   
   
   
   
   
   
   
   • Angle LMN measures 45^o. Erase any extraneous constructions if you so wish.
     
     
     
     
     
     
     
   
   
   
   

Edit Method Two: Starting with a 90 Degree Angle

1. Construct a 90^o angle.
   
   
   
   
   
   
   


2. Bisect the 90^o angle.
   
   
   
   • Upon bisection, you'll be left with two angles, each measuring 45^o.
     
     
     
     
     
     
     
   
   
   
   

Edit Things You'll Need

• Paper


• Pen or Pencil


• Compass


• Straightedge

Edit Related wikiHows

• How to Construct a 60 Degrees Angle Using Compass and Ruler


• How to Construct a 90 Degrees Angle Using Compass and Ruler

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