Final answer:
To find the value of x in a polygon with given angles, we apply the rule that the sum of interior angles in a quadrilateral is 360 degrees. After setting up an equation with the given angles and summing up, we find x to be 27, which is not among the provided options. Hence, there might be a misprint in the options or the problem is not stated correctly.
Step-by-step explanation:
To find the value of x in the polygon with angles 3x, 2x+40, 4x, and x+50, we will use the fact that the sum of the interior angles of a quadrilateral is always 360°. So, we set up the equation:
3x + (2x+40) + 4x + (x+50) = 360°.
Simplify this equation:
3x + 2x + 40 + 4x + x + 50 = 360,
10x + 90 = 360.
Subtract 90 from both sides:
10x = 270.
Now, divide both sides by 10 to find x:
x = 27.
However, as 27 is not one of the provided answer options and we must have made a calculation error. Let's recalculate:
3x + 2x + 40 + 4x + x + 50 = 360,
10x + 90 = 360,
10x = 270,
x = 27. Oh, there is indeed a miscalculation. The correct division should be:
10x = 270,
x = 27.
Upon rechecking we confirm the initial calculation was correct and 27 should be the answer, but as it is not matching the multiple choices provided, the calculation might not be related to this question or the given options are incorrect.