Let $a_1 a_2 a_3 \dotsb a_{10}$ be a regular polygon. A rotation centered at $a_1$ with an angle of $\alpha$ takes $a_4$ to $a_8$. Given that $\alpha < 180^\circ$, find $\alpha,$ in degrees

Question

01-04-2022
Mathematics

Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Let $a_1 a_2 a_3 \dotsb a_{10}$ be a regular polygon. A rotation centered at $a_1$ with an angle of $\alpha$ takes $a_4$ to $a_8$. Given that $\alpha < 180^\circ$, find $\alpha,$ in degrees

Sagot :

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.

5. ¿En qué grupos se integraron lasprimeras comunidades humanas?a)Recolectores, cazadores ypescadores.b) Ingenieros, científicos y cazadores.c) Cazadores, pesca

Bailey has a eyeglasses with a prescription of −4.00 −4.00D. While wearing these glasses so that the lenses sit 2.00 2.00 cm in front of the eyes, Bailey can se

30Select the correct answer"On the other hand" is an example of what?O A.jargonO B.cliché○ C.space filler○ D.transitional deviceResetNext

Question 4 of 10You can bisect an angle using the paper folding technique.A. TrueB. False

There are several m&ms in a bag. There are 18 green, 19 red, 14 blue, 17 orange, 17 brown, and 19 yellow. 1). What is the probability of choosing either a r

The rectangular prism below is split into cubes. Each cube is 15 of an inch on each side. A rectangular prism made up of the described cubes. It is two cubes

Which of these types of fats is stored just underneath the skin?a) Subcutaneous fatb) Surrounding fatc) Cellular fatd) Visceral fat

PSemester ExamQuestion 30 of 40Which number produces a rational number when added to 0.53?OA. 0.2645751311...○ B.B.57○ C. √5○ D. πT← PREVIOUSSUBMIT

King James 1 chartered two British companies in 1606 to colonize America: these companies were to provide the capital and people for the new settlements in Amer

For this activity select a pesticide from your home or go to a local store (Wal-Mart, Target, and Lowe’s). You can also look up pesticide labels on the Interne

sqdancefan sqdancefan · Answer 1 · 2022-04-01T17:34:42-04:00

Answer:

72°

Step-by-step explanation:

The required angle of rotation can be found by considering the regular polygon to be inscribed in a circle. Each of its 10 vertices will be separated by a central angle of 360°/10 = 36°. So, the vertices a8 and a4 will be separated by a central angle of (8 -4)(36°) = 144°.

The angle a4-a1-a8 is an inscribed angle, so will have half the measure of the central angle intercepting the a4-a8 arc. The desired angle of rotation to map a4 to a8 is ...

α = 144°/2 = 72°

maheshpatelvVT maheshpatelvVT · Answer 2 · 2022-05-05T06:38:56-04:00

The value of angle α is 72° if the regular polygon is inscribed in a circle and rotation centered at a_1

What is a regular polygon?

A polygon is a geometric figure with a finite number of sides in two dimensions. A polygon's sides or edges are made up of straight-line segments that are joined end to end to form a closed shape. The vertices or corners are the points where two line segments meet, and an angle is generated as a result.

Consider the regular polygon to be inscribed in a circle to get the required angle of rotation.

A center angle of 360°

=360°/10 = 36°

It will separate each of its 10 vertices.

The central angle:

= (8 - 4)×(36°) = 144°

An inscribed angle is a4-a1-a8:

So α will be:

α = 144/2 ⇒ 72°

Thus, the value of angle α is 72° if the regular polygon is inscribed in a circle and rotation centered at a_1

Learn more about the regular polygon here:

https://brainly.com/question/11810316

#SPJ4

Let $a_1 a_2 a_3 \dotsb a_{10}$ be a regular polygon. A rotation centered at $a_1$ with an angle of $\alpha$ takes $a_4$ to $a_8$. Given that $\alpha < 180^\circ$, find $\alpha,$ in degrees

Sagot :

What is a regular polygon?

Other Questions