If the sum of interior angle measures of a polygon is \( 720^{\circ} \), how many sides does the polygon have? A. 4 B. 7 C. 6 D. 5

To find the number of sides of a polygon given the sum of its interior angle measures, we can use the formula: \[ \text{Sum of interior angles} = (n - 2) \times 180^{\circ} \] where \( n \) is the number of sides of the polygon. Given that the sum of interior angle measures is \( 720^{\circ} \), we can set up the equation: \[ (n - 2) \times 180^{\circ} = 720^{\circ} \] Now, we can solve for \( n \) to find the number of sides of the polygon. Solve the equation by following steps: - step0: Solve for \(n\): \(\left(n-2\right)\times 180=720\) - step1: Multiply the terms: \(180\left(n-2\right)=720\) - step2: Divide both sides: \(\frac{180\left(n-2\right)}{180}=\frac{720}{180}\) - step3: Divide the numbers: \(n-2=4\) - step4: Move the constant to the right side: \(n=4+2\) - step5: Add the numbers: \(n=6\)