Question

2. The inner angle of a regular
polygon is 165°. How many sides does it have​

Answer 1

Answer:

24 sides

Step-by-step explanation:

Since, the measure of each interior angle is 165°, we have,

$⇒\frac{180°(n-2)}{n}=165°$

$⇒180°(n-2)=165°n$

$⇒180°n-360°=165°n$

$⇒180°n-165°n=360°$

$⇒15°n=360°$

$⇒n=\frac{360}{15}$

$⇒<u>n=24</u>$

Hence, the regular polygon with interior angle each measuring 165 degrees is a 24-side polygon..