1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
liberstina [14]
3 years ago
8

Help with inscribed polygons. Me and my daughter do not understand this.

Mathematics
1 answer:
erastovalidia [21]3 years ago
8 0

Answer:

Part 1)

a.1) The central angle of pentagon is 72°

a.2) The central angle of hexagon is 60°

a.3) The central angle of decagon is 36°

a.4) The central angle of dodecagon is 30°

b.1) The measure of each interior angle of pentagon is 108°

b.2) The measure of each interior angle of hexagon is 120°

b.3) The measure of each interior angle of decagon is 144°

b.4) The measure of each interior angle of dodecagon is 150°

Part 2) The central angle and the interior angle are supplementary angles

Part 3) As the number of sides increases, the central angle decreases and the interior angle increases.

Step-by-step explanation:

Part 1. For each polygon, include the following information in the paragraph box below:

a) What was the central angle you used to locate the vertices? Show your calculation.

we know that

To find the central angle divide 360 degrees by the number of sides of the polygon

case a.1) Pentagon

The pentagon has 5 sides

so

The central angle is equal to

360°/5=72°

case a.2) Hexagon

The pentagon has 6 sides

so

The central angle is equal to

360°/6=60°

case a.3) Decagon

The pentagon has 10 sides

so

The central angle is equal to

360°/10=36°

case a.4) Dodecagon

The pentagon has 12 sides

so

The central angle is equal to

360°/12=30°

b) What is the measure of each interior angle of the polygon? Show your calculation

we know that

The sum of the interior angle of the polygon is equal to

S=(n-2)*180°

where

n is the number of sides

To find each the measure of each interior angle, divide the sum of the interior angles by the number of sides

case b.1) Pentagon

The pentagon has 5 sides

so

S=(n-2)*180°

S=(5-2)*180°=540°

Divide by the number of sides

The measure of each interior angle is equal to

540°/5=108°

case b.2) Hexagon

The hexagon has 6 sides

so

S=(n-2)*180°

S=(6-2)*180°=720°

Divide by the number of sides

The measure of each interior angle is equal to

720°/6=120°

case b.3) Decagon

The hexagon has 10 sides

so

S=(n-2)*180°

S=(10-2)*180°=1,440°

Divide by the number of sides

The measure of each interior angle is equal to

1,440°/10=144°

case b.4) Dodecagon

The hexagon has 12 sides

so

S=(n-2)*180°

S=(12-2)*180°=1,800°

Divide by the number of sides

The measure of each interior angle is equal to

1,800°/12=150°

Part 2. What is the relationship between the central angle and the interior angle?

we know that

The sum of the central angle plus the interior angle is equal to 180 degrees

therefore

The central angle and the interior angle are supplementary angles

<em>Verify</em>

Pentagon

72°+108°=180°

Hexagon

60°+120°=180°

Decagon

36°+144°=180°

Dodecagon

30°+150°=180°  

Part 3. As the number of sides increases, how do the angles change?

we know that

As the number of sides increases, the central angle decreases and the interior angle increases.

You might be interested in
Which value of m makes the inequality 10m-5&lt;45
mamaluj [8]

Answer:

m < 5

Step-by-step explanation:

10m-5 < 45

Add 5 to both sides

10m - 5 + 5 < 45 + 5

Simplify

10m < 50

Divide both sides by 2

10m/10 < 50/10

Simplify

m < 5

<u><em>Kavinsky</em></u>

5 0
2 years ago
I will mark brainlest <br><br> What is (-5) - (-98)<br><br> lol I am just doing this for fun
denpristay [2]

Step-by-step explanation:

( - 5) - ( - 98) \\ ( - 5) + 98 = 93

6 0
3 years ago
Read 2 more answers
How many diagonals can be drawn from one vertex of a hexagon
Dmitrij [34]
Three diagonals can be drawn in a hexagon mmyyy dude.
5 0
3 years ago
Read 2 more answers
Hi can anyone do this for me please do it on a piece of paper
Vsevolod [243]

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

We don't know the drivers' names or when or where they started. We have made the assumption that the second equation pertains to Kylie.

Each line is plotted with the appropriate slope and y-intercept. The slope is the coefficient of x, and represents the "rise" for each unit of "run" to the right.

8 0
3 years ago
Convert rational numbers to their equivalent decimals
olya-2409 [2.1K]

Answer:

 In order to change a rational number to a decimal, we just convert the number into the form of a fraction. We then divide the numerator with the denominator and find out the exact value of the division.

7 0
2 years ago
Other questions:
  • 3. You purchase a car using a $20,000 loan with a 5% simple interest rate.
    5·1 answer
  • What is 265,200 rounded to the nearest hundred thousand
    10·2 answers
  • Emilia wrote a total of 12 pages over 4 hours. After spending 6 hours writing this week, how
    14·1 answer
  • If a single fair die is rolled, find the probability of the following result.
    14·1 answer
  • Can you help me with these two thank you
    5·2 answers
  • An online store that sells baseballs and bats offers free shipping on any order of $20 or more. The baseballs cost $1 each and t
    8·1 answer
  • Please help will give brainlist!​
    9·1 answer
  • For spirit week at whoville Middle School students were encouraged to wear the school colors of burgundy and gold of the 1,500 s
    11·1 answer
  • Please help asap....​
    6·1 answer
  • Please help!!!!!!!!!
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!