Construct an angle of 52 1/2 degree

First we will construct 105 degree and then bisect it.
Construct 105 degree angle using Ruler and Compass
The following steps are carried out to construct 105 degree angle.

Step 1: Draw a ray with end point  A and B using a ruler.

Ray

Step 2: With A as center and any radius, draw an arc cutting the ray at point C using a compass.

Radius

Step 3: With C as center and the same radius, draw an arc cutting the arc drawn at D.

Arc Radius

Step 4: With D as center and the same radius, draw  an arc again intersecting the previously drawn arc at E.

Arc Intersecting

Step 5: Now, take any radius and draw two arcs with D and E as centers. Let these two arcs intersect at a point F.

Arc Radius

Step 6: Join AF ∠FAB obtained is the angle of measure of 90 degree. 

Angle of Measure

Step 7: The line AF intersect the arc at the point named as G. 

Line Intersect

Step 8: With G and E as center draw an arc with same radius. The arc intersect at the point P.

Arc Radius

Step 9: Join the point P and A. ∠PAB obtained is the angle of measurement 105 degree with reference to reference line AB.

Angle of Measurement

Step 10:105 degree angle.

105 Degree Angle
Now bisecting this angle will give angle 105/2 degree


 

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Draw the angles of 90 and 120 and bisection between 90 and 120 so we will get the angle of 105. Now construct the angle bisector of 105 .We will get the angle of 52 1/2 degree.
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