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.

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