Final answer:
The chord length of 52m cannot exist within a circle that has a radius of only 10m, hence it's not possible to calculate the sector angle with the given values as it's a geometrically impossible scenario.
Step-by-step explanation:
To calculate the angle of the sector OAB in a circle with a radius of 10m and a chord length of 52m, we can use the cosine rule for triangles or the formula for the angle subtended by a chord at the center of the circle. However, we can quickly determine that the given chord length cannot exist in a circle with a radius of 10m, because the chord cannot be longer than the diameter of the circle (which is twice the radius, 20m in this case). Therefore, none of the provided options (a) 60 degrees, (b) 90 degrees, (c) 120 degrees, (d) 150 degrees are correct, as the situation described is geometrically impossible.