Construct a 30˚Angle from a 60˚Angle
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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