Question

Construct a 45º angle just by using a ruler and a compass.

Answer 1

• Step 1: Draw a line segment OA

• Step 2: With center O and any radius, draw an arc which intersect OA at P.

• With center P and the same radius, draw an arc which intersects the previous arc at Q.

• With center Q and the same radius, draw an arc which is intersecting at R.

• Step 3: With centers R and Q and radius more than 1/2 RQ draw arcs intersecting each other at M and join OM which intersect the arc RQP at B.

• Step 4: With center B and P draw arcs which intersect at N.

• Step 5: Join ON

The obtained angle ∠NOA is the angle bisector of the right angle ∠MOA. Hence it is 45°.