Question

Draw ∠ABC of measures 135^°and bisect it.

Answer 1

Steps of Construction:

1. Draw a line of convenient length. Take a point B on it. With B as centre, draw an arc that cuts the line at points X and Y. 
2. With X as centre, cut an arc at P on the previous arc. 
3. With P as centre and same radius in the compass, cut another arc at Q. 
4. With P and Q as centres, cut intersecting arcs and name it as point E. Join EB.
5. With O and Y as centres, draw intersecting arcs and name the intersection point A. Join AB. 
Here, ∠ABC is the required angle of measure 135^°. 

With R and X as centres, form intersecting arcs which meet at point G. 
Here, BG is the required bisector of ∠ABC.

Answer 2

Steps of Construction:

1. Draw a line of convenient length. Take a point B on it. With B as centre, draw an arc that cuts the line at points X and Y. 
2. With X as centre, cut an arc at P on the previous arc. 
3. With P as centre and same radius in the compass, cut another arc at Q. 
4. With P and Q as centres, cut intersecting arcs and name it as point E. Join EB.
5. With O and Y as centres, draw intersecting arcs and name the intersection point A. Join AB. 
Here, ∠ABC is the required angle of measure 135^°. 

With R and X as centres, form intersecting arcs which meet at point G. 
Here, BG is the required bisector of ∠ABC.