Four rods are hinged at their ends to form a convex quadrilateral with sides of length 3, 4, 5 and 6 (in that order). Investigate the different shapes that the quadrilateral can take.

Suppose one angle is 60 degrees as shown in the diagram. Calculate the other angles of the quadrilateral. You might like to check your answer by drawing the quadrilateral accurately, using ruler and compasses only, and then measuring the angles.

Now calculate the angles of the cyclic quadrilateral formed by keeping the lengths of the sides the same and changing the angles so that opposite angles add up to 180 degrees.