Answer:
20 sides
Step-by-step explanation:
The formula that relates interior angles with number of sides is:
[tex]Each \ Interior = \frac{(n-2)*180}{n}[/tex]
Where
n is the number of sides.
We know each interior is 162 degrees, so we substitute and cross multiply and solve for n:
[tex]Each \ Interior = \frac{(n-2)*180}{n}\\162=\frac{(n-2)180}{n}\\162n=(n-2)180\\162n=180n-360\\18n=360\\n=20[/tex]
THus, the polygon has 20 sides
