Questions: The central angle of a regular pentagon measures 180 degrees.

Solution Steps

To determine if the statement is true or false, we need to calculate the central angle of a regular pentagon. The central angle of a regular polygon can be found using the formula: \( \frac{360}{n} \), where \( n \) is the number of sides. For a pentagon, \( n = 5 \).

The central angle of a regular polygon with \( n \) sides is given by the formula: \[ \text{Central Angle} = \frac{360^\circ}{n} \]

For a regular pentagon, \( n = 5 \). Substituting into the formula, we have: \[ \text{Central Angle} = \frac{360^\circ}{5} = 72^\circ \]

The statement claims that the central angle of a regular pentagon measures \( 180^\circ \). From our calculation, the central angle is \( 72^\circ \), which is not equal to \( 180^\circ \).

Final Answer