Construction of 36° angle and 72° angle
- Author:
- moroplogo
- Topic:
- Angles
The construction with ruler and compass of a decagon or a regular pentagon can be carried out by constructing the angle of 36° whose cosine is equal to .
In this activity you can follow, by clicking on Start the steps to construct the 36° and 72° angles.
- Let A and B two points whose distance AB is 1.
- By drawing a circle with center B and radius AB, we place a point C symmetrical to A in relation to B.
- Similarly, we place the point D symmetrical to B in relation to C.
- We raise the perpendicular to (AB) to B noted By using the intersection of two circles of radius AC centred in A and C. Similarly, we draw the perpendicular to (AB) in C noted Cy .
- We place a point E on Cy such that CE=AB, it follows that AE= .
- We draw a circle with center E and with radius CE.
- This intersects the line (AE) at F.
- The circle with center A and radius AF intersects the line By at G and H.
BÂG)=AB/AG=
then the angle BÂG is 36° and the angle GÂH is 72°.
From these angles we can construct a decagon and a regular pentagon.