An isosceles, obtuse triangle has one angle with a degree measure that is 50$\%$ larger than the measure of a right angle. What is the measure, in degrees, of one of the two smallest angles in the triangle? Express your answer as a decimal to the nearest tenth.
An angle with measure $50\%$ larger than the measure of a right angle has measure $\frac{3}{2}\cdot 90^{\circ}=135^{\circ}$.

Thus the other two angles have a combined measure of $45^{\circ}$. Each one has a measure of

$$\frac{45^{\circ}}{2}=\boxed{22.5^{\circ}}.$$