Final answer:
The interior angles of a pentagon add up to 540 degrees. The equation derived from the given angles suggests that x = 68, but this is not in the provided options, indicating a possible typo in the question as one angle is missing.
Step-by-step explanation:
The question is asking to solve for the variable x in the given angles of a pentagon. To find x, we should first know that the sum of the interior angles of a pentagon is 540 degrees because the formula for the sum of interior angles of any polygon is (n-2)*180, where n is the number of sides. In the case of a pentagon, n is 5. Therefore:
- (5 - 2) * 180 = 3 * 180 = 540 degrees
We are given four angles: 100, 3x + 30, 2x - 10, and 80 degrees. There is a missing angle, but since the sum must be 540, we can write the equation:
100 + (3x + 30) + (2x - 10) + 80 + missing angle = 540
We know four angles and only the expression for a single angle is missing, so let's add the known angles together:
100 + 80 + 3x + 30 + 2x - 10 = 540
Combine like terms:
5x + 200 = 540
Subtract 200 from both sides:
5x = 340
Now divide both sides by 5 to solve for x:
x = 68
However, this does not match any of the options provided. This indicates a typo in the original problem, as there should be five angles given for a pentagon, but only four were provided in the question.