Most everything has been explained here. The wire is rated for current capacity based on insulation type but also wire type, aluminum or copper, per NEC 310-16. We won't go into variations of this based on how the wire is used, direct burial, in free air, or in conduit, or derating based on the number of current carrying wires in conduit as these items don't apply. One item that was missed is that the circuit is based on ALL components. This includes the tempurature rating of the terminations. You must use whatever component has the LOWEST temperature rating as the means of determining what chart to use. Just replace the breaker and the recepticle with UL rated components that have the correct amperage ratings for your dryer and you will not only be safe but following the NEC. IF the wire is aluminum you need to apply a de-oxidizing compound to the wire were you make it up at the breaker and at the recepticle. If it is copper you don't.