Final answer:
To find the largest angle in the pentagon, we can use the formula for the sum of interior angles of a polygon and the given information about the arithmetic sequence. However, there seems to be an error in the given information or calculations.
Step-by-step explanation:
To find the measure of the largest angle in the pentagon, we can use the formula for the sum of the interior angles of a polygon, which is (n-2) * 180, where n is the number of sides of the polygon. Since we have a pentagon, n is 5.
We are given that the interior angles form an arithmetic sequence with a common difference of 10 degrees and the smallest angle is 100 degrees. So, we can write the angles as:
100, 100 + 10, 100 + 2*10, 100 + 3*10, 100 + 4*10
Now, we can find the sum of these angles and subtract it from the sum of interior angles of a pentagon to find the largest angle:
Largest angle = (n-2) * 180 - (100 + (100 + 10) + (100 + 2*10) + (100 + 3*10) + (100 + 4*10))
Simplifying the expression, we get:
Largest angle = 5 * 180 - (500 + 550 + 600 + 650 + 700) = 900 - 3000 = -2100 degrees
However, angles cannot be negative, so there must be an error in the given information or calculations.