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

In a parallelogram, opposite angles are equal and consecutive angles are supplementary. This means that if you have an angle measuring \( k \), the angle directly across from it will also be measured as \( k \). Therefore, if another angle in the parallelogram is given (let’s say \( 2k + 10^\circ \)), you can set up the equation \( k + (2k + 10) = 180 \) to solve for \( k \). Simplifying, you’ll find \( 3k + 10 = 180 \), leading to \( 3k = 170 \) and thus \( k = \frac{170}{3} \approx 56.67^\circ\). Another fun fact about parallelograms? If you draw the diagonals of a parallelogram, they bisect each other. This means the point where the diagonals intersect is the midpoint for both; it’s like a secret meeting spot for the angles! So, not only can you find angle \( k \), but you’ll also learn a nifty property about the geometry of shapes that keep their opposite sides and angles equal!