Final answer:
The difference between the average degree measures of the angles in an octagon and a decagon is 9 degrees.
Step-by-step explanation:
An octagon has 8 sides, so it has 8 angles. Similarly, a decagon has 10 sides and 10 angles.
The sum of the degree measures of all angles in an octagon can be found by using the formula (n-2) * 180, where n is the number of sides. For an octagon, this equation becomes (8-2) * 180 = 1080 degrees.
The sum of the degree measures of all angles in a decagon can be found using the same formula, which gives (10-2) * 180 = 1440 degrees.
The average of the degree measures of all angles in an octagon is therefore 1080 divided by 8, which is 135 degrees.
The average of the degree measures of all angles in a decagon is 1440 divided by 10, which is 144 degrees.
So, the difference between the average degree measures of the angles in an octagon and a decagon is 144 - 135 = 9 degrees.