Question

Construct an acute angle and draw bisector of its supplement.

Answer 1

An acute angle is an angle less than 90 degree. So draw any acute angle. you may construct it using compass and ruler or use a protractor or just draw an angle.
2. One way to draw is, draw a straight line AB Mark any point O on that and draw an angle which is less than 90 degrees.
3. Angle DOB is your required acute angle.
4. Since line AB is a straight line, angle DOA is the supplement of angle DOB.
5. Draw an angle bisector for angle DOA
a. With a suitable radius, draw an arc cutting DO and OA.at N and M.
b. With same or larger radius, draw an arc with M as center and then draw another arc with N as center.
c. The intersection point of these 2 arcs be L.
d. Join L and O to get the bisector of angle DOA.
This is the required bisector of the supplement of angle DOB, which is an acute angle

Answer 2

First of all we will draw the arm PQ. Then place the point of the compass at P and draw an arc that passes through Q. Then we will place the point of the compass at Q and draw an arc that passes through P.  Let this arc cut the arc drawn at R. Draw an arc that is centered at the vertex of the angle. This arc can have a radius of any length. However, it must intersect both sides of the angle. We will call these intersection points P and Q This provides a point on each line that is an equal distance from the vertex of the angle.  Draw two more arcs. The first arc must be centered on one of the two points P or Q. It can have any length radius. The second arc must be centered on whichever point (P or Q) you did NOT choose for the first arc. The radius for the second arc MUST be the same as the first arc. Make sure you make the arcs long enough so that these two arcs intersect in at least one point. We will call this intersection point X. Every intersection point between these arcs (there can be at most 2) will lie on the angle bisector. Draw a line that contains both the vertex and X. Since the intersection points and the vertex all lie on the angle bisector, we know that the line which passes through these points must be the angle bisector.