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Angle Measures of Polygons

Question 15 • *STPSB_Geometry 2627 Treigle

To find the measure of the exterior angles, we can subtract the sum of the measures of the interior angles from the sum of the measures of the linear pairs. Therefore, we have , which is equal to 360°.

Answer
A
180 – 180n
B
180n – (n – 2)
C
180 – 180(n – 2)
D
180n – 180(n – 2)

Explanation

Each of the n interior angles and its exterior angle form a linear pair, so the sum of the linear pairs is 180n°. The interior angles sum to 180(n − 2)°, so subtracting gives 180n − 180(n − 2) = 360°. This matches choice D, 180n − 180(n − 2).

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