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Find the sum of 8 exterior angles of a 24-sided regular polygon.
115°
135°
140°
120°
120°
Since it is a regular polygon, all exterior angles are equal. Simply calculate one exterior angle as 360°/24 and multiply by 8.
A regular polygon with n = 24 sides. We need to find the sum of any 8 exterior angles.
E=n360°
Since it is a regular polygon, all exterior angles are equal. Simply calculate one exterior angle as 360°/24 and multiply by 8.
Students often try to use the formula for interior angles (n−2)×180° or confuse the sum of all exterior angles (360°) with the sum of a specific subset of exterior angles.
Calculate the measure of one exterior angle
In any regular polygon with n sides, each exterior angle is given by 360°/n. Given n=24, we find the value for one angle.
Exterior Angle=24360°=15°
Sum the required number of exterior angles
The problem asks for the sum of 8 such exterior angles. Since the polygon is regular, all exterior angles are identical (15° each).
Sum=8×15°=120°
D is correct because the measure of a single exterior angle of a 24-sided regular polygon is 15°, and the sum of 8 such angles is 120°.
Always remember that the sum of ALL exterior angles of any convex polygon is always 360° regardless of the number of sides, which is a useful property for checking geometry problems.
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