Constructing an Angle of 45 Degrees

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To construct an angle of 45°,start by constructing a right angle. To construct a right angle usethe circle theorem which says that a triangle inscribed in a circle,one edge of which is a diameter, is always a right angled triangle.

Therefore, start by drawing a circle with a compass. The centre ofthe circle will be at the position of the compass needle.

Draw a diameter of the circle. Put the compass needle on one endof this diameter and draw an arc which crosses the circle at somepoint.

This point will be a vertex of the triangle. The other twovertices are the ends of the diameter. Join up the vertices. Thevertex where the arc cuts the circle is the right angle.

The angle at A is a right angle, and bisecting thiswill give an angle of 45°. Putthe compass point at A and draw an arc which crosses the other twosides of the triangle.

From where the arccrosses the sides of the triangle, without altering the compasslength, draw extra arcs.

Draw a line fromthe right angle at A to the point where the arcs cross. This linewill bisect the right angle, resulting in two angles of 45°each.