1. **Stating the problem:** We have two adjacent parallelograms sharing a bottom angle, with the top left angle of the upper parallelogram given as $41^\circ$ and the top right angle as $118^\circ$. We need to find the measure of the bottom angle where the two parallelograms meet. 2. **Recall properties of parallelograms:** In any parallelogram, opposite angles are equal, and adjacent angles are supplementary (sum to $180^\circ$). 3. **Identify angles in the upper parallelogram:** Given the top left angle is $41^\circ$, the adjacent top right angle is $118^\circ$ (which matches the given), confirming the parallelogram's angles. 4. **Find the bottom angles of the upper parallelogram:** Since adjacent angles sum to $180^\circ$, the bottom left angle is $$180^\circ - 41^\circ = 139^\circ$$ and the bottom right angle is $$180^\circ - 118^\circ = 62^\circ$$. 5. **Focus on the bottom angle formed by the two parallelograms:** The bottom angle marked by an arc is the angle between the bottom right angle of the upper parallelogram ($62^\circ$) and the adjacent angle of the lower parallelogram. 6. **Since the two parallelograms are adjacent, the bottom angle is the sum of the two adjacent angles at the bottom:** The bottom right angle of the upper parallelogram is $62^\circ$, and the bottom left angle of the lower parallelogram is equal to the top left angle of the lower parallelogram (which is $41^\circ$ by parallelogram properties). 7. **Calculate the bottom angle:** $$62^\circ + 41^\circ = 103^\circ$$. **Final answer:** The bottom angle formed by the two adjacent parallelograms is $103^\circ$.