1. **Problem Statement:** We are given two congruent quadrilaterals GHIJ and MNOP with various side lengths and angles. We need to find the measure of angle $\angle M$ in quadrilateral MNOP. 2. **Key Concept:** Congruent polygons have all corresponding sides and angles equal. This means $\angle M = \angle G$, $\angle N = \angle H$, $\angle O = \angle I$, and $\angle P = \angle J$. 3. **Given Data:** - $\angle G = 72^\circ$ - $\angle N = 143^\circ$ - $\angle P = 61^\circ$ - $\angle O = 84^\circ$ 4. **Using the property of quadrilaterals:** The sum of interior angles in any quadrilateral is $$\angle M + \angle N + \angle O + \angle P = 360^\circ$$ 5. **Substitute known angles:** $$\angle M + 143 + 84 + 61 = 360$$ 6. **Simplify:** $$\angle M + 288 = 360$$ 7. **Solve for $\angle M$:** $$\angle M = 360 - 288 = 72^\circ$$ 8. **Conclusion:** The measure of $\angle M$ is $72^\circ$, which matches $\angle G$ as expected for congruent polygons. **Final answer:** $\boxed{72^\circ}$