Question 824774
{{{n}}}= number of sides in the polygon
The sum of the measures of all interior angles is
{{{(n-2)*180^o}}} .
So if one interior angle measures {{{260^o}}} ,
and the {{{n-1}}} remaining interior angles measure {{{160^o}}} each,
for the sum of all measures in degrees we can write the equation
{{{260+(n-1)*160=(n-2)*180}}}
 
Solving:
{{{(n-2)*180=260+(n-1)*160}}}
{{{180n-360=260+160n-160}}}
{{{180n-160n=260-160+360}}}
{{{20n=460}}}
{{{n=460/20}}}
{{{highlight(n=23)}}}