Question

Construct 37.5° using ruler and compasses.

Answer 1

Steps of Construction:

Construct a line segment PQ

Considering P as centre and any radius, construct an arc which intersects the line PQ at the point R

Considering R as centre and any radius, construct an arc which intersects the previous arc at the point S

Considering S as centre and same radius, construct an arc which intersects the arc in step 2 at the point T

Considering T and S as centre and radius more than half of TS, construct arcs which intersects each other at the point U

Join the points PU which intersects the arc in step 2 at the point V

Considering V and S as cenntres and radius more than half of VS, construct arcs which intersect each other at the point W

Join the points PW and ∠WPQ = 75^o

Bisect the ∠WPQ

Therefore, we know that ∠ZPQ = 37.5^o