Question 202530
You can start with the formula for the sum (S) of the interior angles of a polygon with n sides:
{{{S = (n-2)*180}}} In this problem, you have a pentagon so n =5.
The sum of the interior angles can be expressed as:
{{{S = 4x+4x+4x+3x+3x}}} Add up the x's.
{{{S = 18x}}} Now set this equal to {{{(n-2)*180}}} where n = 5 (for pentagon).
{{{(5-2)*180 = 18x}}}
{{{3*180 = 18x}}} Divide both sides by 18.
{{{3*10 = x}}} so that...
{{{x = 30}}}
The angle at vertex A is 3*x, so...
{{{3x = 3*30}}}={{{90}}}
{{{highlight(A = 90)}}}