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Q: Is it possible to construct an angle of 22.5 degrees using a compass and a straightedge?
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What is the most direct use of a compass in geometry construction?

A compass is used to construct a perfect circle of 360 degrees.


How do you draw an angle of 20 degrees with a compass and a ruler?

to construct an angle of 20 degrees all you have to do is to trisect an angle of 60degrees


How do you construct the bisector of an interior angle of a regular pentagon?

Each interior angle will be 108 degrees then with a compass and a straight edge it can be bisected into 54 degrees.


How do you construct a perpendicular bisector of each side of a parallelogram?

With a compass and a straight edge and the lines must bisect each other at 90 degrees


How do you make 40 degree angle using compass and ruler what is the maths behind it?

Using a protractor rather than a compass is easier as follows:- Draw a straight line of about 8 cm then place a protractor onto the line with zero degrees at the beginning of the line then mark off 40 degrees. Remove the protractor and join the mark to the beginning of the straight line and 'hey presto!' you have constructed a 40 degree acute angle. ---------------------------- It isn't possible to construct a 40 degree angle with only a straightedge and compass. There are well-known constructions for making a 60 degree angle and a 90 degree angle. Building on this, you can make an angle of any multiple of 15 degrees by adding and/or subtracting these angles. If you successively bisect these angles, you get angles of 30, 15, 7.5, 3.75, ... and 45, 22.5, 11.25, ... etc. degrees. Unfortunately there is no way to combine these angles to get exactly 40 degrees. If there were a way to trisect an angle, this would open up many more possibilities. For instance if you trisect a 120 degree angle, you get 40 degrees. In traditional geometrical constructions, you are only allowed to use a ruler and straightedge - a ruler with no marks on it. The Greeks made this rule several centuries BC. For at least 2500 years people have tried to find a way to trisect an angle, but no one has succeeded. If you change the word "straightedge" to "ruler", (all you really need to do is make a pencil mark on the straightedge), then there is a method, but it isn't considered a construction, and it's not really accurate because you have to juggle the position of the ruler until it fits in a certain position.

Related questions

How do you construct 75 degrees with a pair of compass?

gbhgjgh


Is it possible to construct angle 45 With the help of a ruler and a compass?

Yes. First draw a perpendicular (90 degrees) and then bisect the angle.


What is the most direct use of a compass in geometry construction?

A compass is used to construct a perfect circle of 360 degrees.


How do you construct a 270 degree angle with a compass?

90 degrees multiplied by 3...


Two angles that can be trisected with a straightedge and compass are a 90 degrees angle and what other degree of angle?

45 and 90 degree angles


How do you draw an angle of 20 degrees with a compass and a ruler?

to construct an angle of 20 degrees all you have to do is to trisect an angle of 60degrees


How do you draw an angle of 90 degrees?

Use a protractor or construct 2 perpendicular lines with a compass and a straight edge


How do you construct angles without using protractor?

you might not be able to construct all the angles, but using a compass you can construct some angles by constructing angular bisectors. eg:construct angular bisector of straight line i.e; 180 degrees it gives 90 degrees


How do you construct the bisector of an interior angle of a regular pentagon?

Each interior angle will be 108 degrees then with a compass and a straight edge it can be bisected into 54 degrees.


How do you construct a perpendicular bisector of each side of a parallelogram?

With a compass and a straight edge and the lines must bisect each other at 90 degrees


How do you make 40 degree angle using compass and ruler what is the maths behind it?

Using a protractor rather than a compass is easier as follows:- Draw a straight line of about 8 cm then place a protractor onto the line with zero degrees at the beginning of the line then mark off 40 degrees. Remove the protractor and join the mark to the beginning of the straight line and 'hey presto!' you have constructed a 40 degree acute angle. ---------------------------- It isn't possible to construct a 40 degree angle with only a straightedge and compass. There are well-known constructions for making a 60 degree angle and a 90 degree angle. Building on this, you can make an angle of any multiple of 15 degrees by adding and/or subtracting these angles. If you successively bisect these angles, you get angles of 30, 15, 7.5, 3.75, ... and 45, 22.5, 11.25, ... etc. degrees. Unfortunately there is no way to combine these angles to get exactly 40 degrees. If there were a way to trisect an angle, this would open up many more possibilities. For instance if you trisect a 120 degree angle, you get 40 degrees. In traditional geometrical constructions, you are only allowed to use a ruler and straightedge - a ruler with no marks on it. The Greeks made this rule several centuries BC. For at least 2500 years people have tried to find a way to trisect an angle, but no one has succeeded. If you change the word "straightedge" to "ruler", (all you really need to do is make a pencil mark on the straightedge), then there is a method, but it isn't considered a construction, and it's not really accurate because you have to juggle the position of the ruler until it fits in a certain position.


How many degrees in a directional compass?

there are 360 degrees in a compass