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.



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



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



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



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.



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



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



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



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



Step 10:105 degree angle.


Now bisecting this angle will give angle 105/2 degree