Find the measure of BCA

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

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