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Constructing a 30° angle
This shows how to construct a 30° angle from scratch using a compass and straightedge.
If you already have one of the angle sides given, you can skip the first step.
This construction is essentially the construction of a 60° angle which is then
bisected to make 30°, but
with parts of the two steps combined.
Also see:
Constructing a 45° angle
Constructing a 60° angle
Instructions Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping.
(If there is no image below, see support page.)
Step-by-step Instructions
| Step 1 |
Draw a line segment which will become one side of the angle.
(Skip this step if you are given this line.) The exact length is not important. Label it PQ. P will be the angle's vertex. |
| Step 2 |
Set the compass on P, and set its width to any convenient setting. |
| Step 3 |
Draw an arc across PQ and up over above the point P. Label the point where it crosses PQ as point S. |
| Step 4 |
Without changing the compass width, move the compass to the point S.
Draw a broad arc that crosses the first one and goes well to the right.
Label the point where the two arcs cross as point T. |
| Step 5 |
Without changing the compass width, move the compass to the point T, and draw an arc across the previous arc,
creating point R. |
| Step 6 |
Draw a line from P to R. |
| Step 7 |
Done. The angle QPR has a measure of 30° |
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Try it yourself
Click here for a printable worksheet containing two 30° angle exercises.
When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.
Other constructions
Lines
Angles
Triangles
Triangle Centers
Circles, Arcs and Ellipses
Non-Euclidean constructions
(C) 2007 Copyright John Page
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