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
Ede4ka [16]
3 years ago
8

Find the sum of the measures of the interior angles of each of the following convex polygons: a pentagon, an octagon, a dodecago

n, a forty-sided polygon, a fifty-two sided polygon, a hundred sided polygon.
Mathematics
2 answers:
Artyom0805 [142]3 years ago
6 0

Answer:

pentagon=540°

octagon= 1080°

decagon= = 1440°

forty-sided polygon= 6840°

fifty-two-sided polygon=9000°

hundred-sided polygon=17640°

Step-by-step explanation:

To find the measure of the sum of the interior angle of a polygon, we will simple use the formula;

sum of interior angle = (n-2)180

where n is the number of sides of the polygon

We are ask to find the sum of the interior angle of a pentagon, octagon, decagon, a forty-sided polygon, a fifty-two-sided polygon and a hundred-sided polygon.

First we need to define some terminology;

A penatgon is a five(5)-sided polygon

An Octagon is an eight(8)-sided polygon

A Decagon is a ten(10)-sided polygon

We can now proceed to solve

sum of interior angle = (n-2)180

Sum of interior angle of a pentagon = (5-2)180

                                                             = 3 × 180

                                                             =540°

Sum of interior angle of a pentagon = 540°

Sum of interior angle of an octagon  = (8-2)180

                                                             = 6 × 180

                                                             =1080°

Sum of interior angle of an octagon = 1080°

Sum of interior angle of a decagon  = (10-2)180

                                                             = 8 × 180

                                                             =1440°

Sum of interior angle of a decagon = 1440°

Sum of interior angle of a forty-sided polygon  = (40-2)180

                                                                               = 38 × 180

                                                                                =6840°

Sum of interior angle of a forty-sided polygon = 6840°

Sum of interior angle of a fifty-two-sided polygon  = (52-2)180

                                                                                    = 50 × 180

                                                                                     =9000°

Sum of interior angle of a fifty-two-sided polygon = 9000°

Sum of interior angle of a hundred-sided polygon  = (100-2)180

                                                                                     = 98 × 180

                                                                                      =17640°

Sum of interior angle of a hundred-sided polygon = 17640°

Margarita [4]3 years ago
5 0
This likely has a pattern. Lets see if we can find it.

The sum of a triangle is 180
The sum of a 4 sided figure is 360
The sum of a 5 sided figure is 3*180 = 540
The sum of a 6 sided figure is 4*180 = 720
==========================
The pattern looks like it it (( n-2 )*180) for any polygon where n is the number of sides of the polygon.

You can convince yourself (but this is not a formal proof) by starting with a 6 sided figure. Pick one point on the figure where 2 sides meet. Draw diagonals to all the points not connected to the point you've chosen. You should be able to get 4 such diagonals. You have created 4 triangles.

4*180 = 720 just what your estimate said.d

8 sides will give 6*180 = 1080 degrees and if you keep going on the above table you will see 1080 come up for 8. I'd post a diagram but I don't know how to upload it.


This procedure is extremely important. There is a new math around where these kinds of problems are solved by reducing them to much simpler questions, and getting an answer for them. The pattern is what you are looking for.

Now you can do the rest of the questions.
Pentagon: (5 - 2) * 180 = 
Octagon: (8 - 2) * 180 =
dodecagon (12 - 2)*180=
40 sides 38*180 =  
100 sides 98 * 180 =
You might be interested in
A bicycle has a listed price of $660.95 before tax. If the sales tax rate is 7.25%, find the total cost of the bicycle with sale
skelet666 [1.2K]

9514 1404 393

Answer:

  $708.87

Step-by-step explanation:

The price with tax included is ...

  660.95 + 0.0725×660.95 = 660.95(1 +0.0725) = 708.87

The total cost of the bicycle with tax is $708.87.

8 0
3 years ago
Read 2 more answers
Can someone help me find the surface area of this.please​
masha68 [24]

Answer:

The surface area is 552 square cm.

7 0
3 years ago
Read 2 more answers
Mr. Gurung sold a bicycle for Rs 18,816 and made a profit of 12%. if he wants
LenaWriter [7]

Answer:

Rs. 23520

Step-by-step explanation:

Given that :

At 12% profit ; sales price = 18,816

At (12 + 3)% profit ; sales price = x

Hence,

0.12 = 18,816

0.15 = x

Cross multiply ;

0.12x = 0.15 * 18816

0.12x = 2822.4

x = 2822.4 / 0.12

x = 23520

Hence, sales price for a 3% increaa in profit should be Rs. 23520

5 0
2 years ago
Select the correct ratios.
Goshia [24]
65:100 because there are 65 girls and then 65 girls + 35 boys = 100 total students
4 0
2 years ago
Find the volume of a square pyramid with base edge = 9 cm
kondaur [170]
16 cm

HHHHHHHHHHHHHHHHHHHHHHHHH
4 0
3 years ago
Other questions:
  • Why is a square always symmetrical
    12·2 answers
  • Minneapolis, Minnesota and Portland, Oregon have very similar latitudes. (Latitude measures how far north or south a place is, w
    11·3 answers
  • A 6-sided number cube is rolled. What is the probability that it will land on a number greater than 2?
    13·1 answer
  • Convert 54 percent to as decimal
    10·2 answers
  • Potatoes cost £9 for a 12.5kg bag at a farm shop.
    9·2 answers
  • 7 * 4 = 28<br>4x7=28<br>28 +7=4<br>?​
    15·1 answer
  • What is the angle "d" pleaseeee???​
    6·2 answers
  • Explain how to multiply two numbers with different signs.
    13·1 answer
  • A rectangular prism has a volume of 144 cubic inches. If the length is 2 times the width and the width is 4, find the height of
    9·2 answers
  • If –3 + i is a root of the polynomial function f(x), which of the following must also be a root of f(x)? –3 – i –3i 3 – i 3i
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!