How to Construct a 30 Degrees Angle Using Compass and Straightedge

Starting with a Ray

Draw a ray AB. Let A be the vertex of the angle we're going to construct.

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.

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).

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.

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. Erase any extraneous constructions if you so wish.Construct a 30 Degrees Angle Using Compass and Straightedge Step 5Bullet1.jpg

a 60 Degree Angle

Construct a 60 angle as described here.

Bisect the 60 angle as described here. Upon bisection, you'll have two angles measuring 30 each.Construct a 30 Degrees Angle Using Compass and Straightedge Step 7Bullet1.jpg