The angle measure of a straight line is 180°, and so if the you know that one angle off of it is (5x)°, then you know that the other section is (180 - 5x)°.
Because it's an isosceles triangle, there are two identical angles, which happen to be the angles with the measure of (5x - 30)° and (180 - 5x)°.
Since they have the same measure, 5x - 30 = 180 - 5x. Solve:
Thus,
x = 21°.