How many sides does a regular polygon have if each exterior angle measures 72 degrees?

2 answers:

7 0

I think you are supposed to divide the sum of the interior angles of the polygon (360 degrees) by the exterior angles of the polygon (72 degrees). When you do this: 360 / 72 = 5 sides.

This would be a pentagon.

damaskus [11]3 years ago

7 0

Answer: 5 sides.

Step-by-step explanation:

We know that the total sum of all exterior angles of a regular polygon = 360°

If each exterior angle measures 72 degrees.

Then the number of sides of the regular polygon

$n=\frac{360^{\circ}}{\text{measure of each exterior angles}}=\frac{360^{\circ}}{72^{\circ}}=5$

Therefore, the regular polygon has 5 sides if each exterior angle measures 72 degrees.

You might be interested in

9α – 8α Can someone please answer this question ty

Andrei [34K]

1a (you don’t necessarily need to include the 1, so you can just put “a” if you’d like).

5 0

2 years ago

A lady walks into a cafe. She order four items. a coffe for 3.28, a bagel for 1.27, a juice for 0.56 and a muffin for 2.33. How

malfutka [58]

She spent $7.44 because 3.28 + 1.27 + 0.56 + 2.33 = 7.44

7 0

2 years ago

Solve using algebraic equation: 5sin2x=3cosx (No exponents)

DaniilM [7]

$5\sin2x=3\cos x\iff10\sin x\cos x=3\cos x$

by the double angle identity for sine. Move everything to one side and factor out the cosine term.

$10\sin x\cos x=3\cos x\iff10\sin x\cos x-3\cos x=\cos x(10\sin x-3)=0$

Now the zero product property tells us that there are two cases where this is true,

$\begin{cases}\cos x=0\\10\sin x-3=0\end{cases}$

In the first equation, cosine becomes zero whenever its argument is an odd integer multiple of $\dfrac\pi2$ , so $x=\dfrac{(2n+1)\pi}2$ where $n[/tex ]is any integer.\\Meanwhile,\\[tex]10\sin x-3=0\implies\sin x=\dfrac3{10}$

which occurs twice in the interval $[0,2\pi)$ for $x=\arcsin\dfrac3{10}$ and $x=\pi-\arcsin\dfrac3{10}$ . More generally, if you think of $x$ as a point on the unit circle, this occurs whenever $x$ also completes a full revolution about the origin. This means for any integer $n$ , the general solution in this case would be $x=\arcsin\dfrac3{10}+2n\pi$ and $x=\pi-\arcsin\dfrac3{10}+2n\pi$ .