1. **State the problem:** We have a parallelogram ABCD with diagonals intersecting at E. The angle at vertex C inside the parallelogram is given as $13x - 16$ degrees, and the adjacent angle at vertex B is $9x + 4$ degrees. We need to find the measure of angle $\angle ADB$. 2. **Recall properties of parallelograms:** In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (sum to 180°). Also, the diagonals bisect each other. 3. **Set up the equation for adjacent angles:** Since angles at B and C are adjacent inside the parallelogram, they satisfy: $$ (13x - 16) + (9x + 4) = 180 $$ 4. **Simplify and solve for $x$:** $$ 13x - 16 + 9x + 4 = 180 $$ $$ 22x - 12 = 180 $$ $$ 22x = 180 + 12 $$ $$ 22x = 192 $$ $$ x = \frac{192}{22} $$ $$ x = \frac{96}{11} $$ 5. **Calculate the angle at C:** $$ 13x - 16 = 13 \times \frac{96}{11} - 16 = \frac{1248}{11} - 16 = \frac{1248}{11} - \frac{176}{11} = \frac{1072}{11} \approx 97.45^\circ $$ 6. **Calculate the angle at B:** $$ 9x + 4 = 9 \times \frac{96}{11} + 4 = \frac{864}{11} + 4 = \frac{864}{11} + \frac{44}{11} = \frac{908}{11} \approx 82.55^\circ $$ 7. **Find $\angle ADB$:** In parallelogram ABCD, $\angle ADB$ is the angle between diagonal $DB$ and side $AD$. Since diagonals bisect each other, triangles $\triangle ADB$ and $\triangle CDB$ are congruent. The angle $\angle ADB$ is equal to the angle at vertex C inside the parallelogram, which is $13x - 16$ degrees. Therefore, $$ m\angle ADB = 97.45^\circ $$ **Final answer:** $$ m\angle ADB \approx 97.45^\circ $$