22. The sum of the interior angles regular polygon is 1440 . Find of a number of sides of the regife 23. A seven sided polygon is called (a) pentagon (b) heptagon hexagon (d) nonagon

Given that the sum of the interior angles of a regular polygon is 1440, we can use the formula for the sum of interior angles of a polygon to find the number of sides. The formula for the sum of interior angles of a polygon is given by: \[ S = (n - 2) \times 180 \] where: - \( S \) is the sum of the interior angles, - \( n \) is the number of sides of the polygon. We are given that the sum of the interior angles is 1440, so we can set up the equation: \[ 1440 = (n - 2) \times 180 \] Now, we can solve for \( n \) to find the number of sides of the regular polygon. Solve the equation by following steps: - step0: Solve for \(n\): \(1440=\left(n-2\right)\times 180\) - step1: Multiply the terms: \(1440=180\left(n-2\right)\) - step2: Swap the sides: \(180\left(n-2\right)=1440\) - step3: Divide both sides: \(\frac{180\left(n-2\right)}{180}=\frac{1440}{180}\) - step4: Divide the numbers: \(n-2=8\) - step5: Move the constant to the right side: \(n=8+2\) - step6: Add the numbers: \(n=10\) The number of sides of the regular polygon is 10. Now, let's move on to the second part of the question. A seven-sided polygon is called a heptagon. Therefore, the correct answer is (b) heptagon.