Question

<1 is the top angle. <2 is the bottom angle. the dot in the middle is 114 degrees. Can someone help, please!! m<1= and m<2=

Answer 1

m∠1 = 57°

m∠2 = 123°

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°