Question 557778
For a polygon with n sides and n angles, the sum of the measures of all the interior angles equals (n-2)180 degrees.
For a polygon whose angles add up to 2520 degrees,
{{{(n-2)180=2520}}} --> {{{n-2=2520/180}}} --> {{{n-2=14}}} --> {{{n=16}}}
We know the measure of 3 of the 16 angles. We have to find the measure of
16-3=13 angles.
If 3 of the angles measured 105.5 degrees, and the 13 remaining angles measure x degrees,
{{{13x+3*105.5=2520}}} --> {{{13x+316.5=2520}}} --> {{{13x=2520-316.5}}} --> {{{13x=2203.5}}} --> {{{x=2203.5/13}}} --> {{{x=169.5}}}
The 13 remaining angles measure 169.5 degrees.