Question

In a convex 20-sided polygon, the sum of the 10 larger interior angles is 160 degrees more than the sum of the 10 smaller interior angles. What is the average measure of the 10 larger interior angles?

Answer 1

Answer: 170

Explanation:

Let L be the sum of the degree measures of the 10 larger interior angles, and S be the sum of the degree measures of the 10 smaller interior angles. The angles in a convex 20-sided polygon add up to 180(20-2)=3240 degrees, which tells us that L+S=3240. The problem also tells us that L-S=160. Adding both equations together, we get $2L=3400, and by dividing by 2, we get L=1700. Therefore, the sum of the 10 larger interior angles is 1700 degrees, and the average measure of these angles is 1700/10

=170

Answer 2

3240 degrees? I guess. I'm sorry if its the wrong answer.