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°.