This question uses inscribed angles. Inscribed angles are angles who's vertexes are on the circumference of the circle. The measure of said angle will be half the amount of the corresponding arc.
b is easily found as 58 degrees using this definition. Similarly, d is 130. Afterwards, it is only a and c. These are both impossible (questionably) to find with the given information unless you factor in that they are both congruent.
The total measure of a circle is 360. Subtract b and d and you get 172. Divide that by 86 for both a and c.
The measure of a's arc is 86 degrees.