2002 AMC 12B Problem 5

Let

v,

w,

x,

y,

and

z

be the degree measures of the five angles of a pentagon. Suppose

v\lt w\lt x\lt y\lt z

and

v,

w,

x,

y,

z

form an arithmetic sequence. Find the value of

x.

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Solution

The five interior angles sum to

540^\circ.

Writing the sequence as

x-2d,

x-d,

x,

x+d,

x+2d,

the sum is

5x=540,

x=108.

Thus, the correct answer is D.

Concepts: angle sum · arithmetic sequence

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.