To solve for \(x\) and \(y\) in the given cyclic quadrilateral, we can use the properties of cyclic quadrilaterals. ### Properties 1. Opposite angles in a cyclic quadrilateral sum to \(180^\circ\). ### Given - \(\angle C = 5x^\circ\) - \(\angle A = 7x^\circ\) - \(\angle D = 9y^\circ\) - \(\angle B = 21y^\circ\) ### Equations From the property of cyclic quadraterals: 1. \(\angle C + \angle A = 180^\circ\) \[ 5x + 7x = 180 \] \[ 12x = 180 \] \[ x = 15 \] 2. \(\angle D + \angle B = 180^\circ\) \[ 9y + 21y = 180 \] \[ 30y = 180 \] \[ y = 6 \] ### Solution - \(x = 15\) - \(y = 6\)