The answer is ∠C = 47°.
First calculate the internal angle of the triangle on the picture:
180° - 137° = 43°.
Because the sum of the angles in a triangle is 180°, the angle A will be 180° - (90° + 43°) = 47°.
Angle A and C are vertical, so they are the same:
∠A = ∠C = 47°.