Let's call it a straight line L 1 if we cross the intersection of a and α on α.

Then L 1 and a can determine a plane.

Then we call the intersection of this plane and β L2.

Then it proves that L 1 and L2 are parallel.

Because a⊥α of a⊥β

So a⊥L 1,a⊥L2.

And L 1 and L2 are on the same plane.

So l1/L2

So α is parallel to β.