Since the triangle we are given is a right angle triangle (notice that two sides are perpendicular to each other) and we are given the measure of another of its angles (angleZ = 47 degrees), then we can calulate the remaining angle via the property that the addition of the three angles of a triangleshould add to 180 degrees:
angleY + angleX + angleZ = 180
90 + angleX + 47 = 180
combining numerical terms:
137 + angleX = 180
subtracting 137 from both sides:
angleX = 180 - 137
angleX = 43 degrees.