Step 1 :Given the figure's markings and \(m \angle A=76^{\circ}\) and \(m \angle B=104^{\circ}\), we are asked to identify which theorem can be used to prove that the quadrilateral is a parallelogram.
Step 2 :In a parallelogram, opposite angles are equal. However, the angles given are not opposite angles, they are adjacent angles.
Step 3 :The sum of adjacent angles in a parallelogram is 180 degrees. Therefore, if the sum of the given angles is 180 degrees, we can use this to prove that the quadrilateral is a parallelogram.
Step 4 :Calculating the sum of the given angles, we find that \(76^{\circ} + 104^{\circ} = 180^{\circ}\). This means that the given angles are supplementary, which is a property of adjacent angles in a parallelogram.
Step 5 :Thus, we can use this property to prove that the quadrilateral is a parallelogram. The theorem that states that if the consecutive angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram, can be used.
Step 6 :Final Answer: \(\boxed{\text{Theorem 34}}\)