In these lessons, we will learn how to construct a 30-degree angle from a 60-degree angle.

**Related Pages**

Constructing Angles

Construct 45° Angles

More Geometry Lessons

We can use the angle bisector method to construct some other angles from existing angles.

**Examples:**

A 30° angle can be obtained by bisecting a 60° angle.

A 15° angle can be obtained by bisecting a 30° angle.

A 45° angle can be obtained by bisecting a 90° angle.

A 22.5° angle can be obtained by bisecting a 45° angle.

**Example:**

The figure shows a point *B* on a straight line. Construct an angle of 30° at point *B*.

**Solution:**

Construct a 60° angle, and then construct an angle bisector to obtain a 30° angle.

Step 1: Stretch the compasses to any width. Put the sharp end of the
compasses at point *B* and draw an arc on the line. Label the point where the arc intersects the line
as point *C*.

Step 2: While keeping the sharp end of the compasses at point *B*,
move the compasses away from C and draw a second arc above the line about mid-way between points *B* and *C*.

Step 3: Without changing the width of the compasses, place the sharp end
of the compasses at point *C* and draw an arc to intersect the second arc.

Step 4: Draw a line from point *B* to the point of intersection of
the 2 arcs. Angle *ABC* is 60˚.

Step 5: We now need to Bisect angle *ABC*. Put the sharp end of your
compasses at point *B* and make one arc on the line *BC* (point *S*) and another arc on line *AB* (point *T*).

Step 6: Without changing the width of your compasses, put the sharp
end of the compasses at *S* and make an arc within the lines *AB* and *BC*. Do the same at *T* and make
sure that the second arc intersects the first arc.

Step 7: Draw a line from point *B* to the points of intersection
of the 2 arcs. This line *MB* bisects .
Angle *MBC* is 30 degrees.

**How To Construct A 45 Degree Angle Using A Compass And Ruler**

Constructing a 45-degree angle can be done by first constructing a 90-degree angle and then bisecting
this 90-degree angle. Make sure you know how to construct an angle bisector and a 90-degree angle
before you attempt constructing a 45-degree angle.

**How to construct a 30 degree angle using a pencil, ruler and a pair of compasses only?**

**How to construct an angle of 30 and 60 degrees?**

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