The value of x in the hexagon given in the image above is: 132°.
What is the Sum of an N-Sided Polygon?
The sum of all interior angles of an n-sided polygon = (n - 2)180, where n is the number of angles/sides of the polygon.
The polygon shown is a hexagon with six (6) interior angles. Find its sum.
Sum of the hexagon = (6 - 2)180
Sum of the hexagon = 720°
This means that if we add the measures of all the six interior angles of the given hexagon, we would get 720°.
Therefore:
x + 108 + 113 + 132 + 75 + 160 = 720
x + 588 = 720
x = 720 - 588
x = 132°
Thus, the value of x in the hexagon given in the image above is: 132°.
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