1. The problem involves a cyclic quadrilateral WXYZ inscribed in a circle, with angles at vertices W and X given as 44° and 24° respectively. 2. In a cyclic quadrilateral, opposite angles sum to 180°. Therefore, angle W + angle Y = 180° and angle X + angle Z = 180°. 3. Given angle W = 44°, we find angle Y by subtracting from 180°: $$\text{angle } Y = 180^\circ - 44^\circ = 136^\circ$$ 4. Given angle X = 24°, we find angle Z similarly: $$\text{angle } Z = 180^\circ - 24^\circ = 156^\circ$$ 5. The red arc XY corresponds to the chord XY, and the angle subtended by this chord at the circumference is related to these angles. 6. The problem asks to find the colored angles, which are 44° at W and 24° at X, and we have found the opposite angles Y = 136° and Z = 156°. Final answers: - Angle Y = 136° - Angle Z = 156°