1. **State the problem:** We are given a parallelogram ABCD with angles labeled as follows: \(\angle D = (x+8)^\circ\), \(\angle A = (y+9)^\circ\), and \(\angle C = (3x)^\circ\). We need to find the values of \(x\) and \(y\). 2. **Recall properties of parallelograms:** Opposite angles in a parallelogram are equal, and adjacent angles are supplementary (sum to 180°). 3. **Set up equations:** - Since \(\angle D\) and \(\angle B\) are opposite, \(\angle D = \angle B\). - Since \(\angle A\) and \(\angle C\) are opposite, \(\angle A = \angle C\). - Adjacent angles sum to 180°, so \(\angle D + \angle A = 180^\circ\). 4. **Use the given angle expressions:** \[ (x+8) + (y+9) = 180 \] Simplify: \[ x + y + 17 = 180 \] \[ x + y = 163 \quad \text{(Equation 1)} \] 5. **Use opposite angles equality:** \[ y + 9 = 3x \quad \text{(since } \angle A = y+9, \angle C = 3x\text{)} \] \[ y = 3x - 9 \quad \text{(Equation 2)} \] 6. **Substitute Equation 2 into Equation 1:** \[ x + (3x - 9) = 163 \] \[ 4x - 9 = 163 \] \[ 4x = 172 \] \[ x = \frac{172}{4} = 43 \] 7. **Find \(y\) using Equation 2:** \[ y = 3(43) - 9 = 129 - 9 = 120 \] 8. **Verify angles:** - \(\angle D = x + 8 = 43 + 8 = 51^\circ\) - \(\angle A = y + 9 = 120 + 9 = 129^\circ\) - \(\angle C = 3x = 3 \times 43 = 129^\circ\) - Check sum of adjacent angles: \(51 + 129 = 180^\circ\) correct. **Final answer:** \(x = 43\), \(y = 120\).