Problem:
Let , and be the degree measures of the five angles of a pentagon. Suppose and , and form an arithmetic sequence. Find the value of .
Answer Choices:
A.
B.
C.
D.
E.
Solution:
A pentagon can be partitioned into three triangles, so the sum of the degree measures of the angles of the pentagon is
The arithmetic sequence can be expressed as , and , where is the common difference, so
Thus, .
The problems on this page are the property of the MAA's American Mathematics Competitions