1. **State the problem:** We are given expressions for the sides of a quadrilateral and need to find the values of $a$ and $b$. 2. **Analyze the quadrilateral:** The quadrilateral has opposite sides marked congruent, meaning it is a parallelogram. Opposite sides are equal in length. 3. **Set up equations:** Since opposite sides are equal, $$3b + 2 = 9a - 11$$ $$6b - 7 = 2a + 3$$ 4. **Solve the system of equations:** From the first equation: $$3b + 2 = 9a - 11$$ $$3b = 9a - 13$$ $$b = \frac{9a - 13}{3}$$ Substitute $b$ into the second equation: $$6\left(\frac{9a - 13}{3}\right) - 7 = 2a + 3$$ Simplify: $$2(9a - 13) - 7 = 2a + 3$$ $$18a - 26 - 7 = 2a + 3$$ $$18a - 33 = 2a + 3$$ Bring all terms to one side: $$18a - 33 - 2a - 3 = 0$$ $$16a - 36 = 0$$ Solve for $a$: $$16a = 36$$ $$a = \frac{36}{16} = \frac{9}{4} = 2.25$$ 5. **Find $b$:** Substitute $a = 2.25$ back into $b = \frac{9a - 13}{3}$: $$b = \frac{9(2.25) - 13}{3} = \frac{20.25 - 13}{3} = \frac{7.25}{3} = 2.4167$$ 6. **Final answer:** $$a = 2.25, \quad b \approx 2.42$$