If ∠a = 35°, what does ∠b equal?

These are complementary angles.

If two angles are complementary, then

the sum of their measures is 90°.

Since we know that one of the angles measures 35°, we can find the measure of the other by taking 90 minus the measure of the original angle which in this case is 90 - 35.

So we have 90° - 35° which is 55°

So the measure of the other angle is 55°