Find the SUM of all interior angles for each polygon. \( \begin{array}{llll}\text { 11) regular dodecagon } & \text { 12) regular heptagon } \\ \begin{array}{llll}\text { A) } 2520^{\circ} & \text { B) } 1620^{\circ} & \text { A) } 1440^{\circ} & \text { B) } 540^{\circ} \\ \text { C) } 1980^{\circ} & \text { D) } 1800^{\circ} & \text { C) } 900^{\circ} & \text { D) } 1260^{\circ}\end{array} \\ \begin{array}{llll}\text { 13) regular quadrilateral } & \text { B) } 1080^{\circ} & \text { 14) regular } 24 \text {-gon } \\ \text { A) } 1260^{\circ} & \text { D) } 540^{\circ} & \text { A) } 3960^{\circ} & \text { B) } 3780^{\circ} \\ \text { C) } 360^{\circ} & \text { C) } 4680^{\circ} & \text { D) } 4860^{\circ}\end{array}\end{array} \)
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To find the sum of all interior angles of a polygon, you can use the formula \( (n - 2) \times 180^\circ \), where \( n \) is the number of sides. For the regular dodecagon (12-sided polygon), the sum of the interior angles is: \[ (12 - 2) \times 180^\circ = 10 \times 180^\circ = 1800^\circ. \] So the answer for the dodecagon is \( D) \, 1800^{\circ} \). For the regular heptagon (7-sided polygon), the calculation is: \[ (7 - 2) \times 180^\circ = 5 \times 180^\circ = 900^\circ. \] Thus, the answer for the heptagon is \( C) \, 900^{\circ} \). For the regular quadrilateral (4-sided polygon), we have: \[ (4 - 2) \times 180^\circ = 2 \times 180^\circ = 360^\circ. \] So, the answer is \( C) \, 360^{\circ} \). For the regular 24-gon, we calculate: \[ (24 - 2) \times 180^\circ = 22 \times 180^\circ = 3960^\circ. \] Hence, the answer is \( A) \, 3960^{\circ}. \)
