Question

the sum of the interior angle measures of a convex polygon is $2340^{circ}$. how many sides does it have?
number of sides = \boxed{}

Explanation:

Step1: Recall interior angle sum formula

The sum of interior angles of an $n$-sided polygon is $(n-2)\times180^\circ$.

Step2: Set up equation with given sum

$$(n-2)\times180 = 2340$$

Step3: Solve for $n$ (divide both sides by 180)

$$n-2 = \frac{2340}{180} = 13$$

Step4: Isolate $n$ (add 2 to both sides)

$$n = 13 + 2 = 15$$

Answer:

15