Answer:
A. 264
Step-by-step explanation:
First, we have to find the value of x. Then we can use that to find the required arc measure.
∠M = (1/2)(arc KN - arc LN)
60 = (1/2)((18x -6) -(5x +17)) = (1/2)(13x -23) . . . . substitute and simplify
120 = 13x -23 . . . . . . . multiply by 2
143 = 13x . . . . . . . . . . add 23
11 = x . . . . . . . . . . . . . . divide by 13
__
arc KNL = (arc KN) + (arc NL) = (18x -6) +(5x +17) = 23x +11
= 23·11 +11
arc KNL = 264 . . . . degrees
5:16 is no
24:15 is no
3:12 is yes
-- If the 55° angle is one of the two equal angles, then
the third angle is 70° .
-- If the 55° angle is the third angle, then each of the two
equal angles is 62.5° .
-- For either of these cases, there are an infinite number
of possible sets of side-lengths.
The statement in the question does not hold water.