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

The measure of each interior angle of a regular heptagon is approximately 128.57°.

Step-by-step explanation:

A regular heptagon has 7 equal sides and 7 equal angles. To find the measure of each interior angle of a regular heptagon, we can use the formula:

angle = (n-2) * (180°) / n

Substituting n = 7 into the formula, we get:

angle = (7-2) * (180°) / 7

angle = 5 * (180°) / 7

Calculating this, we find that each interior angle of a regular heptagon lug nut measures approximately 128.57° when rounded to the nearest degree.

Answer 2

`129^(\circ)`

Step-by-step explanation:

n = Number of sides of a polygon = 7

The interior angles of a polygon is given by

`\theta=((n-2)180^(\circ))/(n)`

`\Rightarrow \theta=((7-2)* 180^(\circ))/(7)`

`\Rightarrow \theta=(5* 180^(\circ))/(7)`

`\Rightarrow \theta=(900^(\circ))/(7)`

`\Rightarrow \theta=128.57^(\circ)\approx 129^(\circ)`

Each interior angle of a heptagonal nut is
`129^(\circ)`.