2002 AMC 12B Problem 5

Below is the professionally curated solution for Problem 5 of the 2002 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2002 AMC 12B solutions, or check the answer key.

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Concepts:angle sum arithmetic sequence

Difficulty rating: 1080

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 $x.$

$72$

$84$

$90$

$108$

$120$

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 $5x=540,$ so $x=108.$

Thus, the correct answer is D.

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