Answer: X equals 8.
Step-by-step explanation: The polygon in the question has 5 sides. However, it is an irregular polygon hence the sides are given as 62 degrees, 66 degrees, 77 degrees, 59 degrees and 12X degrees.
The size of the exterior angle of a polygon is calculated as
Angle = 360/n
Where n is the number of sides. So for a five sided polygon, the size of the exterior angle is calculated as
360/5 which equals 72. Since it is an irregular polygon, the sum of the exterior angles can be expressed as
62 + 66 + 77 + 59 + 12X = 360
264 + 12X = 360
Subtract 264 from both sides of the equation
12X = 96
Divide both sides of the equation by 12
X = 8
