Solve for \( k \) in the parallelogram below. Draw \( (5 k+83)^{\circ} \)

To solve for \( k \) in the parallelogram where one angle measures \( (5k + 83)^{\circ} \), remember that consecutive angles in a parallelogram are supplementary, meaning they add up to \( 180^{\circ} \). This means if one angle is \( (5k + 83)^{\circ} \), the adjacent angle must be: \[ 180^{\circ} - (5k + 83)^{\circ} = 97 - 5k \] Since the opposite angles are equal in a parallelogram, we can set up the equation: \[ (5k + 83) + (97 - 5k) = 180 \] Now combine like terms: \[ (5k - 5k) + (83 + 97) = 180 \] This simplifies to: \[ 180 = 180 \] This tautology indicates that we have a true statement but no specific values for \( k \). Thus, \( k \) can be any value — the equation is satisfied for all \( k \). Hence, the solution is that \( k \) is not restricted to a specific number; it can take any value!