Question

modeling real life a fire hydrant bolt is in the shape of a regular pentagon.
a. what is the measure of each interior angle?
the measure of each interior angle is

b. investigate why are fire hydrants made this way?
fire hydrants are made this way to deter people from tampering with fire hydrants because most wrenches are

Explanation:

Step1: Recall formula for interior angle of regular polygon

The formula for the measure of an interior angle of a regular polygon is \(\frac{(n - 2)\times180^{\circ}}{n}\), where \(n\) is the number of sides. A regular pentagon has \(n = 5\) sides.

Step2: Substitute \(n = 5\) into the formula

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Answer:

a. \(108\)
b. Since the interior angle of a regular pentagon (\(108^{\circ}\)) is not a common angle for standard wrenches (which often have angles like \(90^{\circ}, 120^{\circ}\) etc. for common polygon - shaped nuts/bolts like squares, hexagons). So it deters tampering as most wrenches won't fit the \(108^{\circ}\) - angled (pentagon - shaped) bolts on fire hydrants.