Answer:
6
Step-by-step explanation:
Given information:
Interior angle of a polygon cannot be more that 180°.
One interior angle = [tex]80^{\circ}[/tex]
Other interior angles are = [tex]128^{\circ}[/tex]
Let n be the number of sides of the polygon.
Sum of interior angles is
[tex]Sum=80+128(n-1)[/tex]
[tex]Sum=80+128n-128[/tex]
Combine like terms.
[tex]Sum=128n-48[/tex] .... (1)
If a polygon have n sides then the sum of interior angles is
[tex]Sum=(n-2)180[/tex]
[tex]Sum=180n-360[/tex] .... (2)
Equating (1) and (2) we get
[tex]180n-360=128n-48[/tex]
Isolate variable terms.
[tex]180n-128n=360-48[/tex]
[tex]52n=312[/tex]
Divide both sides by 52.
[tex]n=\frac{312}{52}[/tex]
[tex]n=6[/tex]
Therefore the number of sides of the polygon is 6.
