Construction of an angle bisector of an Angles of 30° and 45°

(1) Construction of an angle bisector of 30°:
Steps:
1. Draw angle ABC = 60°.

• Draw a line segment BC of any suitable length
• With  B as the centre.  draw an arc of any suitable radius that cuts BC at point D.
• With D as the centre and the same radius as taken in step 2, draw one more arc that cuts the previous arc at point E.
• Join BE and produce to any point A.
  : ∠ ABC so obtained is of 60°, i.e., ∠ABC = 60°.
  

2. Construction of an angle bisector

• Draw BP, the bisector of ∠ABC.
  :. ∠PBC = `1/2`∠ ABC = `1/2` × 60° = 30⁰
  

(2) Construction of an angle bisector of 45°:
Steps:
1. Draw angle OBC = 90°

• Draw line segment BC of any length.
• With B as the centre, draw an arc that cuts BC at point D.
• With D as the centre, draw an arc of the same radius to cut the first arc at E.
• With E as centre, draw another arc (same radius) to cut the first arc at F.
• With E and F as centres and a radius of more than half of EF, draw arcs intersecting at point P.
• Join BP and extend it to get point A.
  ∠ABC so obtained is of 90 ⁰ i.e., ∠ABC = 90⁰.
  

2. Construction of an angle bisector

• Draw a line segment BC of any suitable length.
• Construct angle OBC = 90⁰
•  Draw BA, the bisector of angle OBC.
  ∠ ABC so obtained is the angle of 45°.