Question

how many sides does a convex polygon have with the sum for its interior angles. if not possible, answer with the number zero in the box.sum = 3780°sides

Explanation:

Step1: Recall the formula for the sum of interior angles

The formula for the sum of interior angles of a convex polygon with \(n\) sides is \(S=(n - 2)\times180^{\circ}\)

Step2: Substitute the given sum into the formula

We are given that \(S = 3780^{\circ}\). So, we set up the equation \((n-2)\times180=3780\)

Step3: Solve for \(n\)

First, divide both sides of the equation by \(180\): \(\frac{(n - 2)\times180}{180}=\frac{3780}{180}\), which simplifies to \(n-2 = 21\)

Then, add \(2\) to both sides: \(n=21 + 2\)

Answer:

\(23\)