Answer:
sides: 42
name: tetracontadigon
Step-by-step explanation:
The sum of the interior angles of a polygon can be found using the formula:
[tex] \boxed{\boxed{\sf \textsf{Sum of interior angles} = (n - 2) \times 180^\circ}} [/tex]
Where
- [tex] \sf \bold{ n }[/tex] is the number of sides of the polygon.
Given that the sum of the interior angles of the polygon is [tex] \sf \bold{ 7200^\circ }[/tex], we can set up the equation:
[tex] \sf (n - 2) \times 180^\circ = 7200^\circ [/tex]
Now, let's solve for [tex] \sf \bold{ n }[/tex]:
[tex] \sf (n - 2) \times 180^\circ = 7200^\circ [/tex]
Divide both sides by [tex] \sf \bold{ 180^\circ }[/tex]:
[tex] \sf n - 2 = \dfrac{7200}{180} [/tex]
[tex] \sf n - 2 = 40 [/tex]
Add 2 to both sides:
[tex] \sf n = 40 + 2 [/tex]
[tex] \sf n = 42 [/tex]
Therefore, the polygon has [tex] \sf \bold{ \boxed{42} }[/tex] sides. Since it has 42 sides, it is called a 42-gon, or more commonly known as a tetracontadigon.
