The interior angles of a quadrilateral form an arithmetic sequence. If the measure of the largest angle is \(128\) degrees, what is the measure of the second largest angle, in degrees?
If the angles form an arithmetic sequence, then we can create a variable for the difference in angles.
If the largest angle is 128 degrees, then the second largest angle is 128 - x degrees, the third largest is 128 - 2x degrees, and the smallest angle is 128 - 3x degrees.
We also know the interior angle sum of a quadrilateral adds up to 360 degrees.
Therefore, 128 + 128 - x + 128 - 2x + 128 - 3x = 360.
Then we get x = 76/3
Since we are looking for the second largest angle, it is just 128 - 76/3.
Thus, the second largest angle is 308/3 degrees or 102.666666 degrees.