The instantaneous centre of a member lies at the point of intersection of two lines drawn at the ends of the member such that the lines are inclined to the direction of motion of the ends at A. 30° B. 45° C. 60° D. 90°

The correct answer is $\boxed{\text{C}}$.

The instantaneous center of a member is the point at which the member appears to rotate about when it is in motion. It can be found by drawing two lines from the ends of the member such that the lines are inclined to the direction of motion of the ends at 60°.

The following diagram illustrates this concept:

[Diagram of a member with two lines drawn from the ends of the member such that the lines are inclined to the direction of motion of the ends at 60°. The instantaneous center of the member is the point of intersection of the two lines.]

The instantaneous center of the member is the point of intersection of the two lines. This is because the member appears to rotate about this point when it is in motion.

The other options are incorrect because they do not represent the correct angle between the lines drawn from the ends of the member.