Question

each interior angle of a regular polygon measures 156 how many sides does the regular polygon have ?​

Answer 1

Answer: 15

Step-by-step explanation:

Answer 2

`\boxed{n= 15}`

Explanation:

we can use the following formula:

`\alpha = (180(n-2))/(n)`

This formula helps to calculate the sum of the interior angles of a polygon, where:

• 
  `\alpha` = interior angle
• 
  `n` = number of sides

we have the value of the interior angle, and we need "n", so we will solve for "n":

`156= (180(n-2))/(n)\\156n=\frac{180(n-2) \\ot{n}}{\\ot{n}}\\156n= 180n-360\\-24n=-360\\n= 15`

With this we have solved the exercise.

`\text{-B$\mathfrak{randon}$VN}`