Question

how many sides does a regular polygon have if each of its interior angle is 165?​

Answer 1

Answer:

24 sides

Step-by-step explanation:

You know that each of the interior angles is 165 degrees so that gives you half of your equation, 165 times n, or 165n. Second, set your interior angles equal to the interior angle formula (n-2)180 = 165n. Last, solve for n. Divide by 15 to get n = 24 sides to the polygon.

Answer 2

${\huge{\underline{\underline{\sf {\mathfrak{Answer}}}}}}$

${\underline{\underline{\rm {Given:}}}}$

• $Polygon \ is \ regular \ , \ all \ sides \ are \ equal$
• $Each \ angle = 165^0$

${\underline{\underline{\rm {Solution:}}}}$

$By \ formula \ of \ sum \ of \ angles:$

• $Sum \ of \ angles = (n - 2) × 180^0$⠀⠀ n is number of sides
• $165 × n = (n - 2)180^0$⠀⠀⠀⠀⠀ ⠀⠀ (as all angles are equal)
• $165n = 180n - 360^o$
• $15n = 360^0$
• $n = 24$

$\boxed{\implies{\boxed{Number \ of \ sides = 24}}}$