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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

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