The diagram shows two congruent regular pentagons and part of a regular n-sided polygon A. Two sides of each of the regular pentagons and two side of A meet at the pint P. Calculate the value of n.
Answers
Answer:
n=10
Step-by-step explanation:
For a regular polygon with n sides, each interior angle, x, is given by
[tex]x=180\frac{n-2}{n}[/tex]
This can be solved for n
[tex]n=\frac{360}{180-x}[/tex]
For the pentagons
x(5)=180(3/5)=108 degrees.
The angles around P sum to 360, so
2(x(5))+x(A)=360
x(A)=360-2(108)=144.
Substitue in the equation for n.
n=360/(180-144)=10
The number of sides in this polygon is 10.
For any polygon, the sum of interior angles is given as,
[tex]\bold{Sum\ of\ interior\ angles= {(n-2)}\times {180^o}}[/tex]
where,
n = number of sides,
We know that for a pentagon, the number of sides is 5.
thus, substituting the values in the sum of interior angle formula we get,
[tex]{Sum\ of\ interior\ angles= {(n-2)}\times {180^o}}[/tex]
[tex]{Sum\ of\ interior\ angles= {5-2}\times{180^o}}\\= 3 \times {180^o} = 540^o[/tex]
therfore, each angle in a regular pentagon,
[tex]\dfrac{Sum\ of\ interior\ angles}{Number\ of\ Sides} = \dfrac{540^o}{5} = 108^o[/tex],
Let's assume that polygon A is having x number of sides.
At point P, the sum of the angles must be 360°.
The sum of the angles at point P
= interior angle of the first pentagon
+ interior angle of the second pentagon
+ interior angle of the polygon A with x sides
Substituting the values,
360° = 108° + 108° + z
z = 360° - 108° - 108°
z = 144°
Thus, the interior angle of the x sided polygon is z = 144°.
For a regular polygon, all the interior angles are equal,
so, for a polygon with sides x.
the sum of interior angle = measure of interior angle x Number of sides
= [tex]144^o \times x[/tex]
Also, we know
[tex]{Sum\ of\ interior\ angles= {(n-2)}\times {180^o}}[/tex]
Substituting, the values for an x number of side polygon,
[tex]{Sum\ of\ interior\ angles= {(n-2)}\times {180^o}}\\{144^o \times x = {(x-2)}\times {180^o}}\\144x = 180x - 360\\360 = 180x- 144x\\x = \dfrac{360}{36}\\x = 10[/tex]
Hence, the number of sides in this polygon is 10.
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Related Questions
fill in the blanks
1. Hindu deity known as “the Absolute” _______________________.
2. Hindu deity of knowledge and creativity _____________________.
3. Hindu deity that represents transformation of the universe ____________________.
4. Demon king mentioned in the Ramayana ___________________.
5. Hindu deity the represents the creation of the universe ______________________.
6. Hindu deity that represents preservation of the universe _____________________.
7. Hindu deity of good health and prosperity ____________________.
8. Hindu deity of love and devotion ______________________.
Answers
Answer:
I can answer a couple
4. Ravan (i am sure)
5. Bhramha (i think)
6. Vishnu
Step-by-step explanation:
hope this helps!
12 more than the square of a number is the same as 7 times the number.
Answers
Answer: Sorry I don't know
Step-by-step explanation:
Help pls asap I really need help this is confusing
Answers
I need help with this question
Answers
Answer:
j-10=35
j is 45
Step-by-step explanation:
35+10=45
Please help me!!!!
Eight students share 12 mini oatmeal muffins equally and 6 students share 27 mini apple muffins equally.
Carmine is in both groups of students.
What is the total number of mini muffins Carmine gets?
Carmine gets
muffins.
Answers
Step-by-step explanation:
oatmeal 12/8 = 1.5 per student
apple 27/6 = 4.5 per student
carmine gets 1.5 + 4.5 = 6 muffins
Answer:
Step-by-step explanation:
(12 oatmeal)/(8 students) = (1.5 oatmeal)/student
Each student gets 1.5 oatmeal muffins.
(27 apple)/(6 students) = (4.5 apple)/student
Each student gets 4.5 apple muffins.
Carmine gets 1.5 oatmeal plus 4.5 apple = 6 muffins
T-shirts are on sale for 40% off. The original price per t-shirt is $20. What is the total cost, in dollars, of 8 of these t-shirts at the sale price, including an 11% sales tax?
Answers
Answer:
$106.56
Step-by-step explanation:
discounted price of each shirt is $12
12 x 8 = $96 for 8 shirt
96 x 1.11 = $106.56
Regina earns 45 points every time she shops on a certain website. She needs a total of 2,880 points to receive a free item. So far, she has earned 540 points. How many more times will Regina have to shop on the website in order to earn the additional points she needs for a free item?
A.
18
B.
38
C.
52
D.
64
Answers
Answer:
C. 52
Step-by-step explanation:
You can simply subtract 540 from the total amount of points
2880-540=2340
and then you can divide that by the number of points she gets every time she shops on the website
2340÷45
Which would equal 52
So, C. 52 would be the correct answer.
Hope this helps!
what must be added to each term of the ratio 3:5, so that it becomes 4:5
Answers
Answer:
5 must be added to both the terms to get the ratio 4:5.
Step-by-step explanation:
(3+x)/(5+x)=4/5
Therefore,
15+5x=20+4x
=5x-4x=20-15
=x=5
I hope it's helpful!
Answer:
3+y/5+y=4/5
let y be the no.to be added
5(3+y)=4(5+y)
15+5y=20+4y
-5= -y
y=5
How many times greater is the area of Circle 1 than the area of Circle 2?If circle ones radius is 9 and circle twos radius is 3
Answers
It is 9 fr 100% pls trust me
The area of the circle {1} is 9 times greater than circle {2}.
What is Area?
Area is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -
V = ∫∫F(x, y) dx dy
Given is to find how many times greater is the area of circle 1 than the area of circle 2 if circle ones radius is 9 and circle twos radius is 3.
We can write the areas of both the circles as -
A{Ο} = πR²
A{Ο1} = π x 9 x 9
A{Ο2} = π x 3 x 3
We can write -
A{Ο1} / A{Ο2} = {π x 9 x 9} / {π x 3 x 3}
A{Ο1} / A{Ο2} = 9
A{Ο1} = 9A{Ο2}
Therefore, the area of the circle {1} is 9 times greater than circle {2}.
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if (a+b)+(a-b)i=7+2 find a and b
Answers
Answer:
a = 4.5
b = 2.5
Step-by-step explanation:
The question is incomplete.
Complete question
If (a+b)+(a-b)i=7+2i find a and b
Compare the terms on both sides
a+b = 7
a-b = 2
Add both equations
a+a = 7+2
2a = 9
a = 9/2
a = 4.5
Recall:.
a+b = 7
4.5+b = 7
b = 7-4.5
b = 2.5
Evaluate the quotient of 1.05 x 103 and 1 x 103
Answers
Answer:
for the 1st one it is 108.15x
and the 2nd it is 103x
Step-by-step explanation:
1. Use the method described in the activity to find the rational zeros for
-10x3 + 15x+ 16x-12.
Answers
Answer:
-42+31x
Step-by-step explanation:
-30+31x-12
-42+31x
Solve for P:
-11 = p - 9
Answers
Answer:
-2Step-by-step explanation:
Add 9 on both sides.
You'll get -2=p
So -2 = p.
-2 is your answer.
Answer:
-2
Step-by-step explanation:
-11 = p - 9
p = -11 + 9
p = -2
Check:
-11 = -2 - 9
Hope that helps!
what is 3333 x 33 x 23 - 908
Answers
Answer:
2528839
Step-by-step explanation:
your welcome
HELP ......,,,,,...,,.....
Answers
Answer:
6. Not similar.
7. Not similar.
8. Not similar.
Step-by-step explanation:
6. Reduce all ratios to simplest form 16:20 = 4:5 ; 12:15 = 4:5 ; 20:26 = 10:13 not all of the sides follow the same ratio, so the triangles are not similar.
7. None of the side lengths are shown. You can find the missing angles of the triangle however, only one of the angles is congruent to the other, so the triangles are not similar.
8. We know that 2 of the sides of each triangle are congruent, and the angle in between the sides are also congruent, which follows the SAS similarity conjecture. However, given that the sides are congruent, not similar in ratio, I can conclude that the triangles are congruent, not similar.
PS. It would mean the world to me if you could mark me brainliest!
Side note- I am not a professional, I just have done this a few months in the past! Best of luck!
Help pleeeeaase!! Marking most Brainly
Answers
How many real-number solutions does the equation have? - 7x2 + 6x + 3 = 0
Answers
Answer:
How many real-number solutions does the equation have? - 7x2 + 6x + 3 = 0
Step-by-step explanation:
a. B^2-4AC = 36-(-84) = 120.
The discriminant is positive. Therefore, we have 2 real solutions.
b. B^2-4AC = 324-324 = 0. 1 real solution.
Hope this helps!
Monu
Exploring Decimals
What is this number in standard form?
(7 x 100) + (4 x 100 ) + (8 x
1,000)
Enter your answer in the box.
Answers
Answer:
Step-by-step explanation:
700+400+8000
9100
Answer: 9,100
Step-by-step explanation:
[tex](8*1,000)+(4*100)+(7*100)=\\8,000+400+700=\\8,400+700=\\9,100[/tex]
15% of the students in the library have brown eyes. If there are 9 students with brown eyes, How many students are in the library
Answers
Answer:
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
ENGLISH
If you Multiply 9x100 you get 900 then you divide 15 divided by 900 is 60
SPANISH
Si multiplica 9x100 obtiene 900, entonces divide 15 dividido por 900 es 60
Hope this will help you
if 3/4 of a certain number is equal to 4 1/2, find the number
Answers
Answer:
6
Step-by-step explanation:
3/4x = 9/2
4/3 * 9/2 = 36/6
6
The number in the mathematical statement is 6
How to determine the number?Let the number be x.
So, the equation can be represented as:
3/4 * x = 4 1/2
Express the fraction as an improper fraction
3/4 * x = 9/2
Multiply through by 4/3
x = 6
Hence, the number is 6
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Please help me with this question what’s 84 + 6 1/3
Answers
Answer:
90 1/3
Step-by-step explanation:
Answer: Mixed number form = 90 1/3
Decimal form = 90.3 with a repation bar
Actual Form = 271 / 3
Step-by-step explanation:
Pls help me I’ll give brainliest
Answers
Answer:
-2.7<4.5
Step-by-step explanation:
Lizette earns $10 in gas money for driving to babysit and then earns $8 for each hour she
babysits the kids. How much money will she make for 5 hours of babysitting?
Answers
Answer:
$30
Step-by-step explanation:
8 x 5 = 40
40 - 10 = 30
the water supplied by a pump fills a drum of 200 liters in 20 seconds. what is the flow rate of this pump
Answers
Step-by-step explanation:
Water filled in 20 second = 200 liters
Water filled in 1 second = 200 / 20 = 10 liters
The flow rate of the pump is 10 liters per second.
Hope it will help :)
Based on the water the pump supplies in 20 seconds, we can find that the flow rate of the pump is 10 liters per second.
The flow rate is essentially the amount of water the pump supplies per unit amount of time which in this case is seconds.
It can be calculated as:
= Amount of water supplied / Time supplied
= 200 / 20
= 10 liters per second
In conclusion, the pump has a flow rate of 10 liters per second.
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3(n – 1) = 6
How do I solve this equation?
Answers
Answer:
n=3
Step-by-step explanation:
distribute, then add 3 to both sides, then divide both sides by 3
Answer:
n = 3
Step-by-step explanation:
3(n−1)=6
Step 1: Simplify both sides of the equation.
3(n−1)=6
(3)(n)+(3)(−1)=6(Distribute)
3n+−3=6
3n−3=6
Step 2: Add 3 to both sides.
3n−3+3=6+3
3n=9
Step 3: Divide both sides by 3.
3n/3 = 9/3\
n= 3
does anybody know what to do here?
Answers
Answer:
m=6
Step-by-step explanation:
38+8m+4=90
42+8m=90
8m=90-42
8m=48
m=6
ILL MARK U BRAINLEST Find the circumference of the circle. Use 3.14 for 1. Round to the nearest hundredth, if necessary.
is
9 in.
The circumference of the circle is about
inches.
1
Answers
Answer:
The answer is either 56.55in or 28.27
Step-by-step explanation:
This is the formula that I used
C=2πr
Circumference = 2·π·4.5 ≈ 28.27433 or
Circumference = 2·π·9 ≈ 56.54867
The answer can be either one. It depends on if 9 is the radius or the diameter of this circle. If 9 is the radius, then the answer would be 56.55in. If the radius isn't 9 but 9 is the diameter, then your radius would be 4.5 and the answer would be 28.27in.
Hope that helps :)
The circumference of the circle will be 56.52 inches.
What is a circumference?
The circumference of a circle can be found using the formula:
Circumference = 2πr
Where r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159.
If the radius of the circle is 9 inches, then we can substitute this value into the formula to find the circumference:
Circumference = 2π(9 inches)
Circumference = 18π inches
We can leave the answer in terms of π or approximate it using a decimal approximation for π. Using the value of π rounded to 3.14, we have:
Circumference ≈ 56.52 inches
Therefore, the circumference of a circle with a radius of 9 inches is approximately 56.52 inches or exactly 18π inches.
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help math eeekkkkkkk
Answers
Answer:
Step-by-step explanation:
Simplify, solve, and graph the Inequality: -2(x+6) > - 48
Answers
Answer:
-2 ( x +6) > - 48
x+6.> - 48/2
x +6 > - 24
x > - 24 - 6
x > - 30
There are 15 books on a shelf. 9 of these books are new. The rest of them are used.
Answers
Answer: 7
Step-by-step explanation:
15-9 =
9 10 11 12 13 14 15
1 2 3 4 5 6 7
7 books were used.