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

Related Topics: More Geometry Lessons

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

**Example*** : *

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.

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.

The following video shows how to construct an angle of 30 and 60 degrees.

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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