Find the sum of the interior angles of a dodecagon, that is, a polygon with 12 sides.

Introduction / Context:
This question checks your understanding of polygon angle formulas in plane geometry. The sum of interior angles of a polygon depends only on the number of sides and is a standard formula asked regularly in aptitude and school level exams. Knowing this formula allows you to quickly compute angle sums for any regular or irregular polygon as long as you know how many sides it has.

Given Data / Assumptions:
- The polygon is a dodecagon, which means it has 12 sides.
- We assume it is a simple polygon, not self intersecting.
- We are asked for the sum of all interior angles, not the measure of each individual angle.

Concept / Approach:
The sum of interior angles S of an n sided polygon is given by the formula:
S = (n − 2) * 180 degrees.
This formula can be understood by dividing the polygon into (n − 2) non overlapping triangles, each contributing 180 degrees to the total. For a dodecagon, n = 12, so we simply substitute this value into the formula.

Step-by-Step Solution:
Step 1: Identify the number of sides of the polygon: n = 12 for a dodecagon. Step 2: Recall the formula for the sum of interior angles: S = (n − 2) * 180 degrees. Step 3: Substitute n = 12 into the formula to get S = (12 − 2) * 180 degrees. Step 4: Simplify the expression inside the parentheses: 12 − 2 = 10. Step 5: Multiply 10 by 180 degrees to obtain S = 10 * 180 degrees = 1800 degrees. Step 6: Therefore, the sum of all interior angles of a dodecagon is 1800 degrees.
Verification / Alternative check:
You can visualise a dodecagon by drawing it and dividing it into triangles from one vertex. Connecting one vertex to all other non adjacent vertices creates (n − 2) triangles, which is 10 triangles for n = 12. Each triangle has an angle sum of 180 degrees, and 10 such triangles contribute 10 * 180 degrees = 1800 degrees. This geometric reasoning reinforces the formula and confirms the result.

Why Other Options Are Wrong:
Option a, 1620 degrees, corresponds to (11 − 2) * 180 and would be correct for an 11 sided polygon (hendecagon), not for a dodecagon.
Option c, 1440 degrees, equals (10 − 2) * 180 and would be the sum for a decagon with 10 sides.
Option d, 1260 degrees, corresponds to a 9 sided polygon (nonagon) since (9 − 2) * 180 = 1260 degrees.
Option e, 1980 degrees, does not correspond to the standard formula for any small integer value of n and is included as a distractor.

Common Pitfalls:
A common mistake is to confuse the sum of interior angles with the sum of exterior angles, which is always 360 degrees for any simple polygon. Another error is miscounting n as 10 or 11 instead of 12, or applying (n − 1) * 180 rather than (n − 2) * 180. Carefully remembering the triangle based derivation can help fix the correct formula in mind: every polygon can be decomposed into (n − 2) triangles from one vertex.

Final Answer:
The sum of the interior angles of a dodecagon is 1800 degrees.