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?

Guest Jan 25, 2022

#1**+1 **

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.

proyaop Jan 25, 2022