How to Construct a 30 ° Angle Using Compass and Ruler

Table of contents:

2024 Author: Samantha Chapman | [email protected]. Last modified: 2023-12-17 09:13

This article explains how to draw an angle of 30^or using a ruler and compass in two different ways.

Steps

Method 1 of 2: Using the Radius

Construct a 30 Degrees Angle Using Compass and Straightedge Step 1

Step 1. Draw an AB segment

Assume point A is the vertex of the angle you want to plot.

Construct a 30 Degrees Angle Using Compass and Straightedge Step 2

Step 2. Position the tip of the compass exactly on point A, then draw an arc that intersects segment AB at any point (called X)

The arc just drawn will be called Arco Uno. To perform the next steps, keep the same opening as the compass without changing it.

Construct a 30 Degrees Angle Using Compass and Straightedge Step 3

Step 3. Place the tip of the compass on point X, then draw a second arc (named Arc Two) that intersects Arc One at the point named Y

Construct a 30 Degrees Angle Using Compass and Straightedge Step 4

Step 4. At this point, position the tip of the compass on point Y and draw another arc (called Arc Tree) that intersects Arc Two at point Z which is in the part of the arc furthest from the vertex A of the corner

Construct a 30 Degrees Angle Using Compass and Straightedge Step 5

Step 5. Now connect points A and Z with a straight line and extend it beyond point Z to form the AC side of the corner

The amplitude of the CAB angle is 30^or. At this point, if you wish, you can erase all the construction lines you needed to draw the corner.

Construct a 30 Degrees Angle Using Compass and Straightedge Step 5Bullet1

Method 2 of 2: Use a 60 ° angle

Construct a 30 Degrees Angle Using Compass and Straightedge Step 6

Step 1. Build an angle of 60^or using the procedure described in this article (in this case, use the point Y indicated in the previous method to trace the AC side of the angle and thus obtain an amplitude of 60 °).

Step 2. Plot the bisector of the angle of 60^or following the procedure described in this article.

Since the bisector of an angle is the straight line that divides it into two equal parts, you will get two identical angles with an amplitude of 30^or each.

Construct a 30 Degrees Angle Using Compass and Straightedge Step 7Bullet1

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