Step 1 :In a parallelogram, opposite angles are equal. Therefore, the measure of angle W is equal to the measure of angle U.
Step 2 :We can set up an equation to solve for p, using the given expressions for W and U: \(2p + 81 = p + 99\).
Step 3 :Solving this equation gives \(p = 18\).
Step 4 :Substituting \(p = 18\) into the equation for W gives \(W = 2*18 + 81 = 117\).
Step 5 :Final Answer: The measure of angle \(W\) is \(\boxed{117}\) degrees.