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
A full grown German Shepherd weighs about 35 kg on Earth and only 13.3 kg on Mars. How much would a German Shepherd puppy weigh
7nadin3 [17]

Answer:

Step-by-step explanation:5 pounds

35/13.3=2.63. 1.9x2.63=5kg

6 0
3 years ago
Mr. Sanchez bought 2 magazine for 9.95 each and 1 book for 14.95 if the sales tax is 6% what is the total cost of Mr. Sanchez pu
Dima020 [189]
Rst you have to find the price of everything together

2 magazines for 9.95 each and a book for 14.95

9.95 + 9.95 + 14.95 = 34.85

Next you convert the percent to a decimal

6% = 0.06

Now you put a one in the ones place

1.06

Multiply this by the cost of everything

34.85 * 1.06 = 36.94

The answer is $36.94

Hope this helps!

Read more on Brainly.com - brainly.com/question/10235412#readmore
5 0
3 years ago
An ice cream cone is 5" deep and 2" in top diameter. One scoop of vanilla ice cream, 2" in diameter, is placed on the cone. If t
Ratling [72]
If the total volume of the ice cream exceeds the internal volume of the cone, then it will overflow.

Volume of icecream = 4/3 * pi * r^3 = 4/3*pi*(1)^3 = 4.189 cu. in.Volume of cone = 1/3 * pi * r^2 * h = 1/3*pi*(1)^2*5 = 5.236 cu. in.

Since Volume of cone > Volume of icecream, the cone will not overflow.

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
5 0
3 years ago
A used car costs $6,472. A down payment of $1,000 is required. The remaining balance is to be paid in 36 equal monthly payments.
blondinia [14]
The answer should be $152.

$6,472 - $1,000 = $5,472
Divide $5,472 by 36 and you end up with $152.
8 0
3 years ago
The dashed line is given by the equation y=-9/5x-4
Svetlanka [38]

If you're looking for the dashed line, here it is.


8 0
2 years ago
Other questions:
  • Lines l and m are parallel and intersected by transversals t and s as shown in the figure below.
    9·1 answer
  • What is 8/16 in simplest form
    15·2 answers
  • What would f(-5.2) equal if f(x)=[[x]]​
    5·1 answer
  • Angle A is in standard position and terminates in quadrant IV. If sec(A) = 4/3 , complete the steps to find cot(A).  Use the ide
    8·2 answers
  • What Is the GCF of the group 6x-3?
    12·1 answer
  • 6(3x - 2) + 5(x + 6)
    13·1 answer
  • What is the simplest form for 15:25​
    13·1 answer
  • 5.46 in fraction form HURRY
    10·2 answers
  • Huilan is 11 years older than Thomas. The sum of their ages is 65. What is Thomas's age?
    10·1 answer
  • Part 1 of 2
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!