Question

How to construct 67.5 degree angle with the help of compass and ruler?? how to construct 37.5 degree angle with the help of ruler and compass??

Answer 1

Draw AB horizontally of some convenient length. Then draw the perpendicular bisector COD  of  AB to meet AB at O.

Now draw the angular bisector OD  of angle AOC.  The angle DOC is 45 deg. Hence, angle DOB is 135 deg.  Now draw an angular bisector of angle DOB to get 67.5 deg.

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37.5 deg.

Draw AB horizontally. Then draw COD perpendicular bisector of AB. Now draw the two trisector lines for the angle COB (90 deg).  So we get OE and OF angles separated by 30 deg.

FOB = 60 deg.  and EOB = 30 deg.   

Draw an angular bisector OG  of angle COB.  Then angle GOB = 45 deg.

Now draw an angular bisector OH of angle GOE, that is in the middle of OG and OE.   The angle HOB will be 37.5 deg.