CST Level 1 Land Surveyor Certification Practice

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Prepare for the CST Level 1 Land Surveyor Certification. Study using flashcards and multiple-choice questions with detailed hints and explanations. Ace your exam!

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What formula is used to calculate the interior angle of a polygon?

(N-2) x 180
N x 180
(N+2) x 180
N / 2 x 180

The correct answer is: (N-2) x 180

The formula to calculate the interior angle of a polygon is derived from the fact that the sum of the interior angles of an N-sided polygon can be determined by the formula (N-2) x 180 degrees. This is based on the concept that a polygon can be divided into triangles, and since each triangle has a sum of angles equal to 180 degrees, the total number of triangles formed by drawing diagonals from one vertex to the other vertices is (N-2). Hence, multiplying the number of triangles by 180 gives the total sum of the interior angles of the polygon. For example, a triangle (3-sided polygon) would have (3-2) x 180 = 1 x 180 = 180 degrees total interior angle, while a quadrilateral (4-sided polygon) would have (4-2) x 180 = 2 x 180 = 360 degrees. This approach works for any polygon, confirming the correctness of the formula used in the answer. In contrast, the other options do not correctly represent the relationship between the number of sides and the sum of the interior angles. For instance, multiplying the number of sides directly by 180 does not account for the necessary subtraction represented in the correct formula