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What is the measure of each interior angle of a regular hexagon?

A. 180°
B. 144°
C. 120°
D. 60°

Sagot :

To determine the measure of each interior angle of a regular hexagon, follow these steps:

1. A regular hexagon has 6 sides.
2. The formula to find the sum of the interior angles of any polygon is given by:

[tex]\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \][/tex]

where [tex]\( n \)[/tex] is the number of sides of the polygon.

3. For a hexagon, [tex]\( n = 6 \)[/tex]. Plugging this value into the formula:

[tex]\[ \text{Sum of interior angles} = (6 - 2) \times 180^\circ = 4 \times 180^\circ = 720^\circ \][/tex]

4. Since a regular hexagon has all equal interior angles, the measure of each interior angle can be found by dividing the sum of the interior angles by the number of sides:

[tex]\[ \text{Measure of each interior angle} = \frac{720^\circ}{6} = 120^\circ \][/tex]

Therefore, the measure of each interior angle of a regular hexagon is [tex]\( 120^\circ \)[/tex]. Hence, the answer is:

C. 1200