### Instruction: The measure of an interior angle of a regular decagon is how many degrees greater than the measure of an interior angle of a regular pentagon?### Response: I know that a regular decagon has 10 congruent interior angles and a regular pentagon has 5 congruent interior angles.
I also know that the sum of the interior angles of any n-sided polygon is (n-2)*180 degrees.
So, the sum of the interior angles of a decagon is (10-2)*180 = 1440 degrees, and the sum of the interior angles of a pentagon is (5-2)*180 = 540 degrees.
Therefore, each interior angle of a decagon is 1440/10 = 144 degrees, and each interior angle of a pentagon is 540/5 = 108 degrees.
To find the difference, I subtract the smaller angle from the larger one: 144 - 108 = 36 degrees.
So, the measure of an interior angle of a regular decagon is 36 degrees greater than the measure of an interior angle of a regular pentagon.