How do you find the curent of a stream when you are given the speed of the boat and the angle in which it is pointed

I think you need one more piece of information. I suspect that you have been given the angle of the boat (with respect to the stream current), the speed of the boat wrt the water, and the speed of the boat wrt the ground. This is a problem in addition (or subtraction) of vectors.

Velocity is speed plus direction. If you have two velocities, regardless of what direction they are in, they can be added together. Say you're on a train moving west at 3mph. Inside the train, you get up and walk across the aisle (north) at 4mph. While moving, what is your total velocity with respect to the ground? Draw an arrow pointing west with length 3. From the head of this arrow, draw another pointing north with length 4. Measure the distance from the tail of the first arrow to the head of the second. The length of this arrow is your total speed, and the angle is your direction. Velocity is speed plus direction.

Your problem is probably very similar, but with the hypotenuse and one of the sides given. Also, the angle is not a right angle. No matter. You should know enough trigonometry to solve for the third side of a triangle, given two sides and an angle.

If the speed of the boat you mean the speed at the given angle, this would be the resultant of the speed of the boat in the water directed straight across, and the speed of the current at right angles, or down stream. If that is the case the take the angle and resolve the speed into its components.