Newton's First Law: Qualitative definition of Force. If no NET EXTERNAL FORCE acts on an object, the object will neither change direction nor its speed, nor both.
Start: What is the net external force in your problem?
What are the forces acting on the object? Gravity and Friction.
Check: Are they acting on the same direction? Yes or No.
In this case: No.
If No, then are they acting perpendicular to each other? No.
If No, then the component of the Gravity and Friction in the direction of motion (in this case sliding). Component of gravity parallel to direction of motion = Weight * sin_theta (where theta is the angle the motion surface makes with horizontal).
Friction is acting parallel to the surface of the motion, but always acts against (opposite) the motion. So, it is mu_k(coef. of kinetic friction) * component of force normal to the surface of motion.
The component of force normal to the surface of motion = Weight * cos_theta (where theta is the angle the motion surface makes with horizontal).
Net external force (=net driving force) = difference between aforemention two forces = Gravity component in the direction of motion - friction force on the surface of motion(note it always acts against motion) = W * sin_theta - mu_k* W*cos_theta
Now, what is second law of motion (Newton's second law). Force = mass * acceleration. Similarly, apply newton's third law of motion: action (= net driving force) = reaction (i.e. mass * acceleration)
So, mass* acceleration = driving force = W * sin_theta - mu_k* W*cos_theta (replace W by mass*g )
So, mass* acceleration = mass*g * sin_theta - mu_k* mass*g *cos_theta
cancel mass from the equation because it is common.
Solve this equation for mu_k (coefficient of friction) = (g * sin_theta - acceleration )/ (g *cos_theta)
You are done. Note, if you get mu_k negative, then what is your interpretation? As I said above, friction always acts against the motion. You must think it and make you interpretation correctly. Friction is a non-conservative force. If you get negative coefficient of friction, the net driving force is not enough to counter the friction, and therefore, there is acceleration, but decceleration. If the object is not in motion as an initial condition, then you will know know kinetic friction. Your answer is "not enough information". Period.