A regular polygon has interior angle $ 160^\circ $.How many sides does it have?
A regular polygon has interior angle $ 160^\circ $.How many sides does it have?
एक नियमित बहुभुज का आंतरिक कोण $160^\circ$ है। इसके कितने भुजाएँ हैं?
Detailed Solution & Logic
Correct Answer:
18
We are given a regular polygon with an interior angle $160^\circ$ and need to find the number of sides $n$.
The formula for the interior angle of a regular polygon is:
$ \text{Interior angle} = \frac{(n-2) \cdot 180}{n} $
Set it equal to $160$:
$ \frac{(n-2) \cdot 180}{n} = 160 $
Multiply both sides by $n$:
$ (n-2) \cdot 180 = 160 n $
180n - 360 = 160n
20n = 360
n = 18
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