The sum of the angles in a pie chart is 360°, as it represents a full circle. Given that four angles are 30°, 45°, 60°, and 90°, their total is \(30° + 45° + 60° + 90° = 225°\).

Now, let the two remaining angles be \(2x\) and \(x\), where \(2x\) is twice the size of \(x\), and they are in a 2:1 ratio.

Adding up all the angles:

\(225° + 2x + x = 360°\)

Simplifying:

\(3x = 360° - 225°\)

\(3x = 135°\)

\(x = \frac{135°}{3}\)

x = 45°

So, the smallest angle of the remaining two angles is x = 45°.