Question

A lug nut is used to secure a wheel on a vehicle. Most lug nuts are shaped like regular pentagons or regular hexagons. However, some lug nuts are shaped like regular heptagons (7 sided). What is the measure of each interior angle of a regular heptagon lug nut? Round your answer to the nearest degree

Answer 1

Answer:

$129^{\circ}$

Step-by-step explanation:

n = Number of sides of a polygon = 7

The interior angles of a polygon is given by

$\theta=\dfrac{(n-2)180^{\circ}}{n}$

$\Rightarrow \theta=\dfrac{(7-2)\times 180^{\circ}}{7}$

$\Rightarrow \theta=\dfrac{5\times 180^{\circ}}{7}$

$\Rightarrow \theta=\dfrac{900^{\circ}}{7}$

$\Rightarrow \theta=128.57^{\circ}\approx 129^{\circ}$

Each interior angle of a heptagonal nut is $129^{\circ}$.