Question

How to construct angle 112.5

Answer 1

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Here's one way. Draw a straight approximately horizontal line of length 20cm and construct a perpendicular bisector. To do this, set your compasses to more than half the length of the line (more than 10cm) position the point at one end of the line and draw arcs on either side of the line over its approximate midpoint. Do the same from the other end of the line so that the arcs intersect. Draw a line through the intersection points of the arcs on either side of the line. This line should be perpendicular to the original line and it should bisect it at 10cm. Measure 11cm vertically along the perpendicular from where it intersects the horizontal line and measure 7cm from this intersect on one side of the horizontal line. Mark the point. Join the top of the measured perpendicular to this point. You should have a right-angled triangle with sides 11cm (vertical) and 7cm (horizontal), the exterior angle of which (where the hypotenuse meets the horizontal line) should be 122.5 degrees

Answer 2

112.5 = 90 + 22.5 So, first construct 90 degree angle. Then find its angle bisector which is 45 degrees. Then again find the angle bisector of 45 degree... which is 22.5 degrees.