Construct a 30 Degrees Angle Using Compass and Straightedge

Learn to construct a 30^o angle using compass and straightedge by different methods.

Steps

Starting with a Ray

1. Draw a ray AB. Let A be the vertex of the angle we're going to construct.
2. Place the tip of the compass on A and draw an arc which cuts AB at some point (say X). Let's call this arc as Arc One. Retain this width of the compass for the remaining steps.
3. Place the tip of the compass on X and draw another arc (call it Arc Two) which cuts Arc One at some point (say Y).
4. Place the tip of the compass on Y and draw another arc (Arc Three) so as to cut Arc Two at a point (say Z) which is on that side of Arc Two which does not contain the point A.
5. Connect the points A and Z with a straight line and extend it to form a ray AC.
   • The measure of the angle CAB is 30^o. Erase any extraneous constructions if you so wish.

a 60 Degree Angle

1. Construct a 60^o angle as described here.
2. Bisect the 60^o angle as described here
   • Upon bisection, you'll have two angles measuring 30^o each.

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 45 Degrees Angle Using Compass and Straightedge
• Construct a 60 Degrees Angle Using Compass and Ruler