Answer: A) 57
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Step-by-step explanation:
For any convex polygon, the sum of the exterior angles is always 360 degrees.
The exterior angles (5x+12), (10x-37) and (9x+1) add to 360. Use this to solve for x.
(5x+12)+(10x-37)+(9x+1) = 360
(5x+10x+9x) + (12-37+1) = 360
24x-24 = 360
24x = 360+24
24x = 384
x = 384/24
x = 16
The expression 10x-37 is then
10x-37 = 10*16-37 = 160-37 = 123
which is the measure of the exterior angle adjacent to angle BCA
The last step is to subtract this from 180 to get angle BCA itself
angle BCA = 180 - 123 = 57