draw an angle of 45 deg and construct its line of symmetry

Steps of construction

1. Draw a line AB

2. Take a point O on the line AB in between points A and B.

3. Taking point O, draw a semi-circle on line AB which cuts the line AB at C and D respectively

4. From point C, make an arc by opening the mouth of compass and same to be done from point D.

5. The point where both the are cuts each other is P. Join OP.

6. ∠BOP = ∠AOP = 90º. Now draw angle bisector of ∠BOP which will give us ∠BOE which is equal to 45º.

The line of symmetry is a line which divides a figure into two symmetrical parts.

∴ line of symmetry of 45º angle would be its angle bisector.

So the angle of is obtained by taking angle bisector of 45º, which will result in its line of symmetry. The line OF is the required line of symmetry.