Answered

Expand your knowledge base with the help of IDNLearn.com's extensive answer archive. Get the information you need from our experts, who provide reliable and detailed answers to all your questions.

POLYGON PATH In Ms. Rickets' math

class, students made a "polygon path"

that consists of regular polygons of 3, 4,

5, and 6 sides joined together as shown.

Sagot :

All the angles from the polygon path made by the students are;

∠1 = 96°

∠2 = 90°

∠3 = 162°

∠4 = 132°

∠5 = 60°

The images of the polygon are missing and so i have attached them.

  • From the attached image, we can see we have;

Triangle (3 sided polygon)

Square ( 4 sided polygon)

Pentagon (5 sided polygon)

Hexagon (6 sided polygon)

Now, we know that formula for external angle of a polygon with n sides is 360/n.

  • Thus, for the 6-sided polygon, the ∠5 = 360/6

∠5 = 60°

  • Since ∠4 is shared by the pentagon and hexagon, then;

∠4 = (360/5) + 60

∠4 = 72° + 60°

∠4 = 132°

  • Since ∠3 is shared by the square and pentagon, then;

∠3 = 90 + 72

∠3 = 162°

  • ∠2 = 90° because external angles of a square = 360/4 = 90°

The polygon 12345 is a 5 sided polygon and as such;

Sum of interior angles = 180(n - 2)

⇒ 180(5 - 2) = 540°

Thus;

∠1 + ∠2 + ∠3 + ∠4 + ∠5 = 540°

Plugging in the relevant values, we have;

∠1 + 90 + 162 + 132 + 60 = 540

∠1 + 444 = 540

∠1 = 540 - 444

∠1 = 96°

Read more at; https://brainly.com/question/4448932

View image AFOKE88
Your engagement is important to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. IDNLearn.com provides the best answers to your questions. Thank you for visiting, and come back soon for more helpful information.