3 Solve for \( k \) in the parallelogram below.

Below is one way to solve a typical parallelogram problem step by step. (In a parallelogram, opposite angles are congruent and consecutive [adjacent] angles are supplementary.) Suppose you are given that one angle is measured as \( 3k \) (in degrees) and its consecutive angle is measured as \( k + 20 \). (In many such problems the two adjacent angles are expressed in terms of \( k \).) Because they form a linear pair we know that \[ 3k + (k+20) = 180. \] Follow these steps to solve for \( k \): 1. **Set up the equation using the supplementary property:** \[ 3k + k + 20 = 180. \] 2. **Combine like terms:** \[ 4k + 20 = 180. \] 3. **Subtract 20 from both sides:** \[ 4k = 180 - 20, \] \[ 4k = 160. \] 4. **Divide both sides by 4:** \[ k = \frac{160}{4}, \] \[ k = 40. \] Thus, the value of \( k \) is \( \boxed{40} \). --- **Note:** If your parallelogram diagram or problem statement gives different expressions for the angles, use the same idea—that adjacent angles sum to \( 180^\circ \) or that opposite angles are equal—to set up and solve your equation.