Answer:
6 sides
Step-by-step explanation:
The sum of the interior angles of a polygon with n sides is given by:
[tex]\boxed{\begin{array}{c}\underline{\textsf{Sum of the interior angles of a polygon}}\\\\S=(n-2) \times 180^{\circ}\\\\\textsf{where $n$ is the number of sides} \end{array}}[/tex]
We are told that one interior angle of an irregular polygon is 80° and each of the other interior angles is 128°. Since the polygon has n sides, the number of interior angles that are each 128° is (n - 1). Therefore, the total sum of the interior angles can be expressed as:
[tex]80^{\circ} + (n - 1) \times 128^{\circ}[/tex]
Equate this to the general sum of the interior angles:
[tex](n-2) \times 180^{\circ}=80^{\circ} + (n - 1) \times 128^{\circ}[/tex]
Solve for n:
[tex]180n^{\circ} - 360^{\circ} = 80^{\circ} + 128^{\circ}n - 128^{\circ}\\\\180n-360=80+128n-128\\\\180n-360=128n-48\\\\180n-128n=-48+360\\\\52n=312\\\\n=6[/tex]
Therefore, the polygon has:
[tex]\LARGE\boxed{\boxed{\sf 6\; sides}}[/tex]
