Answer:
m∠1 = 57°
m∠2 = 123°
Step-by-step explanation:
∵ ∠1 is inscribed angle and the angle with measure 114° is central angle both subtended by the same arc in the circle
∴ m∠1 = 1/2 (114°) = 57°
∵ The quadrilateral contains ∠1 and ∠2 as vertices with the other two red vertices all of them lie on the circle
∴ This quadrilateral is a cyclic quadrilateral
∴ m∠1 + m∠2 = 180 ( opposite angles in cyclic quad.)
∴ m∠2 = 180 - 57 = 123°
