Answer:
#1) 40°
#2) 68°
#3) 57°
Explanation:
The measure of an angle formed by two tangents, a tangent and a secant or two secants is equal to half the difference between the intercepted arcs.
For #1, arc AC is 140°. This makes the other arc equal to 360-140 = 220°. The difference between the arcs is 220-140 = 80°; half of this is 80/2 = 40°.
For #2, arc CE is 112°. This makes arc CBE 360-112 = 248°. The difference between the two arcs is 248-112 = 136°. Half of this is 136/2 = 68°.
For #3, arc RS is 76° and arc UR is 199°. This makes the remaining arc, SU, 360-(76+199) = 360-(275) = 85.
The measures of the intercepted arcs are then 85 and 199; the difference between them is 199-85 = 114. Half of this is 114/2 = 57°.