### Why do this
problem?

The diagram is not given because it is a good learning experiene
for students to draw their own diagrams. The

problem
calls for simple geometrical reasoning involving angles and similar
triangles. It is a good way in to the wonderful mathematics related
to the golden ratio and the Fibonnaci sequence.

### Possible approach

Offer a selection of examples on 'Golden Mathematics' (see links
below).

### Key questions

What do you know about the angles of a reguar pentagon?

Can you spot any isosceles triangles?

Can you spot any similar triangles? ... any congruent
triangles?

Can you use the geometry to give you an equation involving the
unknown you have to find?

### Possible support

Golden Trail