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.

Steps

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.

Starting with a 90 Degree Angle

1. Construct a 90 Degrees Angle Using Compass and Ruler
2. Bisect the 90^o angle.
   • Upon bisection, you'll be left with two angles, each measuring 45^o.

Things You'll Need

• Paper
• Pen or Pencil
• Compass
• Straightedge

Related Articles

• Construct a 60 Degrees Angle Using Compass and Ruler
• Construct a 90 Degrees Angle Using Compass and Ruler

See also

• Construct a Line Parallel to a Given Line Through a Given Point
• Bisect a Line With a Compass and Straightedge
• Draw a Square
• Construct an Angle Congruent to a Given Angle
• Construct a Perpendicular Line to a Given Line Through Point on the Line
• Construct a 30 Degrees Angle Using Compass and Straightedge
• Construct a 60 Degrees Angle Using Compass and Ruler