How can I draw a 30 degree angle without a protractor?

In the exam you will have a ruler and a pair of compasses, which you can use to construct a 60 degree angle by drawing two arcs. You can then draw two more arcs to bisect that 60 degree angle and make a 30 degree angle. 

Here's how to construct an angle ABC of 30 degrees.

First you build the 60 degree angle - put the point of your compass on point B at the end of a straight line, and draw an arc like this:

(then I'd draw it for them)

Next, keep your compass at the same width and move it to the point where your arc crosses the straight line (labelled A). Draw another arc like this:

(I'll draw this)

Then, to make construct the 60 degree angle, draw a straight line from point B to the point where your two arcs cross, which I will label X. 

(drawing of 60 degree angle)

We'll now bisect this angle, or cut it in half, to make the 30 degree angle. Draw two more arcs, one from point A and one from point B. Make sure they're big enough to overlap, and be very careful to keep the compass open at the same width. 

(diagram)

Label the point at which these two new arcs cross C, and draw a straight line from point B to point C. This will cut the 60 degree angle in half and make a 30 degree angle at ABC.