<p>The measures of the interior angles of a convex polygon of <img alt="$n$" height="8" src="https://latex.artofproblemsolving.com/1/7/4/174fadd07fd54c9afe288e96558c92e0c1da733a.png" width="10" /> sides are in arithmetic progression. If the common difference is <img alt="$5^{\circ}$" height="15" src="https://latex.artofproblemsolving.com/a/4/e/a4e94a4d2b45632cf823bb8c26eb19aec5c70cd3.png" width="19" /> and the largest angle is <img alt="$160^{\circ}$" height="13" src="https://latex.artofproblemsolving.com/e/c/e/ece184b486bcd76cff4e781214deef445d299dbb.png" width="33" />, then <img alt="$n$" height="8" src="https://latex.artofproblemsolving.com/1/7/4/174fadd07fd54c9afe288e96558c92e0c1da733a.png" width="10" /> equals:</p>

Question No: 315

The measures of the interior angles of a convex polygon of $n$ sides are in arithmetic progression. If the common difference is $5^{\circ}$ and the largest angle is $160^{\circ}$ , then $n$ equals:

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Tags: Algebra Geometry

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