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

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

• A. 90 degrees
• B. 120 degrees
• C. 150 degrees
• D. 180 degrees

Answer: (B)

To find the measure of each interior angle of a regular hexagon, one can use the formula for the interior angle of a regular polygon, which is given by: \[ \text{Interior Angle} = \frac{(n - 2) \times 180}{n} \] where \( n \) is the number of sides of the polygon. In the case of a hexagon, \( n = 6 \). Plugging in the value: \[ \text{Interior Angle} = \frac{(6 - 2) \times 180}{6} = \frac{4 \times 180}{6} = \frac{720}{6} = 120 \] This calculation shows that each interior angle of a regular hexagon measures 120 degrees. The reason this value makes sense is that a regular hexagon can be divided into 6 equilateral triangles, each having angles of 60 degrees. The interior angles at each vertex of the hexagon are formed by two of these triangles, leading to an angle of \( 60 + 60 = 120\) degrees. Thus, the correct answer indicates that each interior angle of a regular hexagon measures 120 degrees,

To find the measure of each interior angle of a regular hexagon, one can use the formula for the interior angle of a regular polygon, which is given by:

[

\text{Interior Angle} = \frac{(n - 2) \times 180}{n}

]

where ( n ) is the number of sides of the polygon. In the case of a hexagon, ( n = 6 ).

Plugging in the value:

[

\text{Interior Angle} = \frac{(6 - 2) \times 180}{6} = \frac{4 \times 180}{6} = \frac{720}{6} = 120

]

This calculation shows that each interior angle of a regular hexagon measures 120 degrees.

The reason this value makes sense is that a regular hexagon can be divided into 6 equilateral triangles, each having angles of 60 degrees. The interior angles at each vertex of the hexagon are formed by two of these triangles, leading to an angle of ( 60 + 60 = 120) degrees.

Thus, the correct answer indicates that each interior angle of a regular hexagon measures 120 degrees,