Constructing the angle 75°?

3 Answers
Aug 26, 2016

Bisecting angles twice will give an angle of 75°.


Note that #150° div 2 = 75°#

Construct an equilateral triangle using a compass. Each of the angles is 60°. Extend the base.

Now bisect the angle of 60° to create an angle of 30° inside the triangle. THe adjacent supplementary angle will be 150°,

Bisecting the angle of 150° will give the required angle of 75°.

Aug 26, 2016

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Or simply:
1) Set the 60 degree angle
2) Perform angle addition construction of 60 to 30
3) Perform an angle bisecting construction of the 30 degree angle
4) Voila you have 75 degree angle

The answer assumes you know how to construct a 30 and 60 degree angle.
If you don't then:
1) The first one 60 degree use the equilateral trangle construction method
2) For thew 30:
a) Start from AC
b) From A draw a arc A with radius AC
c) From C draw and arc C with radius CA
d) From the intersection point draw and arc intersecting arc C
e) With straight edge connect A to F, you have the 30 degree
f) Finish with disecting angle #/_FAC# pulling the #90=>75#