I have to be honest, this is the most ridiculously worded question of this type that I have ever seen... ask you teacher, why it was so important to force you to solve it using only one variable?
According to the diagram shown, ∠OPQ = ∠OQP = 18°. If PQT is a tangent to the circle, it can be inferred that line OQ is perpendicular to line QT. Ths shows that ∠OQT = 90°.
