<p>The measures of the interior angles of a convex polygon of <img alt="$n$" height="10" src="https://latex.artofproblemsolving.com/1/7/4/174fadd07fd54c9afe288e96558c92e0c1da733a.png" width="13" /> 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="10" src="https://latex.artofproblemsolving.com/1/7/4/174fadd07fd54c9afe288e96558c92e0c1da733a.png" width="13" /> equals:</p> <p><img alt="$\text{(A) } 9\quad \text{(B) } 10\quad \text{(C) } 12\quad \text{(D) } 16\quad \text{(E) } 32$" height="17" src="https://latex.artofproblemsolving.com/5/5/c/55ca5a005956f081083f3b5a5b220b0bf95a8575.png" width="300" /></p>

Question No: 481

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:

$\text{(A) } 9\quad \text{(B) } 10\quad \text{(C) } 12\quad \text{(D) } 16\quad \text{(E) } 32$

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Tags: Geometry

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