Find the SUM of all interior angles for each polygon. \( \begin{array}{llll}\text { 11) regular dodecagon } & \text { 12) regular heptagon } \\ \begin{array}{llll}\text { A) } 2520^{\circ} & \text { B) } 1620^{\circ} & \text { A) } 1440^{\circ} & \text { B) } 540^{\circ} \\ \text { C) } 1980^{\circ} & \text { D) } 1800^{\circ} & \text { C) } 900^{\circ} & \text { D) } 1260^{\circ}\end{array} \\ \begin{array}{llll}\text { 13) regular quadrilateral } & \text { B) } 1080^{\circ} & \text { 14) regular } 24 \text {-gon } \\ \text { A) } 1260^{\circ} & \text { D) } 540^{\circ} & \text { A) } 3960^{\circ} & \text { B) } 3780^{\circ} \\ \text { C) } 360^{\circ} & \text { C) } 4680^{\circ} & \text { D) } 4860^{\circ}\end{array}\end{array} \)

To find the sum of all interior angles for each regular polygon, we use the formula: \[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \] where \( n \) is the number of sides of the polygon. Let's apply this formula to each of the given polygons: --- ### **11) Regular Dodecagon** - **Number of sides (\( n \))**: 12 \[ \text{Sum} = (12 - 2) \times 180^\circ = 10 \times 180^\circ = 1800^\circ \] **Answer:** **D) \(1800^\circ\)** --- ### **12) Regular Heptagon** - **Number of sides (\( n \))**: 7 \[ \text{Sum} = (7 - 2) \times 180^\circ = 5 \times 180^\circ = 900^\circ \] **Answer:** **C) \(900^\circ\)** --- ### **13) Regular Quadrilateral** A regular quadrilateral is a square. - **Number of sides (\( n \))**: 4 \[ \text{Sum} = (4 - 2) \times 180^\circ = 2 \times 180^\circ = 360^\circ \] **Answer:** **C) \(360^\circ\)** --- ### **14) Regular 24-gon** - **Number of sides (\( n \))**: 24 \[ \text{Sum} = (24 - 2) \times 180^\circ = 22 \times 180^\circ = 3960^\circ \] **Answer:** **A) \(3960^\circ\)** --- ### **Summary of Answers:** - **11) Regular Dodecagon:** D) \(1800^\circ\) - **12) Regular Heptagon:** C) \(900^\circ\) - **13) Regular Quadrilateral:** C) \(360^\circ\) - **14) Regular 24-gon:** A) \(3960^\circ\) --- If you have any further questions or need additional explanations, feel free to ask!