Question 1155788
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(1) using interior angles....<br>
The sum of the interior angles of a polygon with n sides is 180(n-2).<br>
{{{(n/2)170+(n/2)150 = 180(n-2)}}}
{{{(n/2)320 = 180n-360}}}
{{{160n = 180n-360}}}
{{{20n = 360}}}
{{{n = 18}}}<br>
ANSWER: 18 sides<br>
(2) using exterior angles....<br>
Nearly always, a problem like this is easier to solve using the exterior angles, whose sum is always 360.<br>
There are (n/2) exterior angles of 30 degrees and (n/2) of 10 degrees.<br>
{{{(n/2)30+(n/2)10 = 360}}}
{{{20n = 360}}}
{{{n = 18}}}<br>