Answer :
Final answer:
The value of x is found by understanding that the sum of exterior angles in any polygon equals 360 degrees. After subtracting known angles from 360, we find the remaining angle to be 96 degrees, which equals 12x. Dividing 96 by 12, we find x to equal 8.
Explanation:
The subject of this problem is a polygon with 5 sides, also known as a pentagon. This pentagon has been shown with its exterior angles, which are 62 degrees, 66 degrees, 77 degrees, 59 degrees, and 12x degrees. To find the value of x, we must first understand the property of exterior angles in polygons.
The sum of exterior angles in any polygon is always 360 degrees. Thus, if we add up all the known exterior angles and subtract from 360, we can solve for the remaining angle:
360 - (62+66+77+59) = 96
This means the remaining exterior angle, which is represented as 12x, is equal to 96 degrees. To find the numerical value of x, we then divide this remaining angle by 12:
96 / 12 = 8.
Therefore, the value of x in this problem is 8.
Learn more about Exterior angles of polygons here:
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