QUESTION: The sum of the measures of a regular polygon is 4,140°. Find the measure of each exterior angle.​

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STEP-BY-STEP EXPLANATION

1. First, we need to find the number of sides of the polygon. To do this, we will use this formula: (S / 180) + 2 (S = sum of interior angles)
2. Solve. (4, 140 / 180) + 2 = 23 + 2 = 25
3. The number of sides of the polygon is 25. Now that we know that, we now need to find the measure of each exterior angle of that polygon. The sum of exterior angles of polygons is always 360°. This is the formula to get the measure of each exterior angle of a polygon: 360° / n (n = number of sides)
4. Solve. 360° / 25 = 14.4°
5. We have now found our answer! The measure of each exterior angle is 14.4°

ANSWER: 14.4°

=) Hope this helps!