2002 AMC 12B Problem 5

Attempt Problem 5 of the 2002 AMC 12B below, then check your answer against the professionally curated solution 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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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 $x.$

$72$

$84$

$90$

$108$

$120$

Answer: D

Concepts:angle sum arithmetic sequence

Difficulty rating: 1080

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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