Construct a 30˚Angle from a 60˚Angle

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.

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

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