Respuesta :
Answer: Largest exterior angle is 85.44 degrees
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Explanation
Rule: The exterior angles of any polygon always add to 360 degrees
Based on that rule, we simply add up the 8 expressions given to us and set that sum equal to 360. Then we solve for x
(x+12)+(2x-3)+(3x+10)+(3x+15)+(2x-19)+(4x-1)+(4x-10)+(6x) = 360
(x+2x+3x+3x+2x+4x+4x+6x)+(12-3+10+15-19-1-10) = 360
25x+4 = 360
25x = 360-4
25x = 356
x = 356/25
x = 14.24
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Once you determine the value of x, you plug that into each of the 8 exterior angle expressions
- x+12 = 14.24+12 = 26.24
- 2x-3 = 2(14.24)-3 = 25.48
- 3x+10 = 3(14.24)+10 = 52.72
- 3x+15 = 3(14.24)+15 = 57.72
- 2x-19 = 2(14.24)-19 = 9.48
- 4x-1 = 4(14.24)-1 = 55.96
- 4x-10 = 4(14.24)-10 = 46.96
- 6x = 6*(14.24) = 85.44
In short we have these 8 exterior angles
- x+12 = 26.24
- 2x-3 = 25.48
- 3x+10 = 52.72
- 3x+15 = 57.72
- 2x-19 = 9.48
- 4x-1 = 55.96
- 4x-10 = 46.96
- 6x = 85.44
We see that 85.44 degrees is the largest exterior angle (which is the angle that corresponds to the 6x). This makes sense because the 6 is the largest x coefficient compared to something like 2x-3 or 3x+10 which have x coefficients of 2 and 3 respectively.
