Unit 8: Polygons And Quadrilaterals Homework 1: Angles Of Polygons (2024)

Mathematics College

Answers

Answer 1

To calculate the sum of the interior angles of a polygon we must take into account the following formulas: x = (n - 2) × 180°, and y = sum of the interior angles ÷ number of sides.

How to calculate the sum of the interior angles in a polygon?

To calculate the sum of the interior angles of a polygon we must take into account the following formula:

x = (n - 2) × 180°

In this formula the value of n represents the number of sides of the polygon. It should be noted that this formula is used when the polygon is irregular, that is, it does not have all the equal sides.

For polygons that are regular we must use the following formula: x = sum of interior angles ÷ number of sides.

According to the above, if we have an irregular pentagon we could calculate the sum of its internal angles as follows:

x = (5 - 2) × 180°x = 3 × 180°x = 540°

On the other hand, if the pentagon is regular, we apply the formula above and then the second formula as shown below:

x = (5 - 2) × 180°x = 3 × 180°x = 540°

y = 540° ÷ 5y = 108°

Note: This question is incomplete because the question is missing. This is the complete question.

How to Calculate the sum of interior angles in a pentagon?

Learn more about polygon in: https://brainly.com/question/2511126

Related Questions

Please help me with this

Answers

Step-by-step explanation:

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Kayden is a stunt driver. One time, during a gig where she escaped from a building about to explode(!), she drove at a constant speed to get to the safe zone that was 160 meters away. After 3 seconds of driving, she was 85 meters away from the safe zone. Let y represent the distance (in meters) from the safe zone after x seconds and determine the function that represents the situation.

Answers

Answer:

y = 25x - 85

Step-by-step explanation:

Every second (x) that passes by is 25 meters gained, and since she's 85 meters away from the safe distance still, the y intercept is -85.

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This item has two parts.
1.
Mr. Cates, the principal at a local middle school, made a rule that there must be 1 adult
for every 4 students attending a field trip.

Part A. Complete the table to show the number of adults for 12, 24, and 40 students.
Number of Students Number of Adults
4.
12
5.
24
6.
40
7.
There will be 33 students attending a field trip to an art museum.
.
8.
Part B. How many adults would need to attend the trip?
9.

Answers

Answer/Step-by-step explanation:

Part A:

[tex]Key:\left[1 Adult = 4 Student][/tex]

[tex]Formula: Divide[/tex] [tex]by[/tex] [tex]4[/tex]

12 Student = 3 Adult

24 Student = 6 Adult

40 Student = 10 Adult

Part B:

33 Student

Hence, divide 33 by 4 = 8 with a remainder of 1.

Therefore, 8 Adult and for the remainder 1 student either one Adult takes 5 Student or Needed 9 Adult.

Determine the factors of x^2 - 8x + 16.
a) (x + 4) (x - 4)
b) (x - 4) (x - 4)
c) (x + 1) (x + 4)
d) (x - 2) (x - 2)

Answers

The answer is B. (x-4)(x-4)

Answer:

B) (x-4)(x-4)

Step-by-step explanation:

x^2-8x+16

(x-4)(x-4)

Mitchell drew a scale drawing of a house. The hall closet is 6 inches long in the drawing. The
actual closet is 4 feet long. What scale factor does the drawing use?

Answers

Answer:

First, write the scale factor. Next, write ratios to represent the unknown actual length and width of the display to the scale length and width of the display. Then, write two proportions by setting the two length ratios equal to one another and the two width ratios equal to one another. The given unit is feet.

The area of a triangular region is 3,136 sq . cm. if the perpendicular from one vertex to the opposite side is 64 cm, find the length of its base

Answers

area=3136sq.cm

height=perpendicular=64 cm

base=?

area=1/2*base*height

3136=1/2*base*64

therefore,, base=98

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Use reasoning to solve for the unknown number. five is the quotient of 100 / some number what is the number 5 is the quotient of 100 divided by _____.

Answers

Answer: 20

Step-by-step explanation: just do 100/5=20 so do 100/20=5 hope this helps!!

Answer:

Step-by-step explanation:

the guy above me ∧ is correct! Hope this helps! :)

The independent variable is the same as the x values and the _____

Answers

Let X and Y two nonempty sets. ... The variable x is called the independent variable (also sometimes called the argument of the function), and the variable y is called dependent variable (also sometimes called the image of the function.)

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find w=a+bi=[tex]\sqrt{z}[/tex], where a and b are real numbers

[tex]\sqrt{2i}[/tex]

Answers

I assume you're talking about finding the square roots of 2i.

We have

•modulus: |2i| = √(2²) = 2

•argument: arg(2i) = π/2

so that the polar form of 2i is

2i = 2 exp(i π/2)

By DeMoivre's theorem,

√(2i) = √2 exp(i (π/2 + 2πk)/2)

where k = 0 or k = 1.

For k = 0,

√(2i) = √2 exp(i (π/2)/2)

… = √2 exp(i π/4)

… = √2 (cos(π/4) + i sin(π/4))

… = √2 (1/√2 + 1/√2 i)

… = 1 + i

For k = 1,

√(2i) = √2 exp(i (π/2 + 2π)/2)

… = √2 exp(i 5π/4)

… = √2 (cos(5π/4) + i sin(5π/4))

… = √2 (-1/√2 - 1/√2 i)

… = -1 - i

What value of b will make the expressions −12.8x+b and −3.2(4x−2.1)+2.4 equivalent?

Answers

Answer:

b = 9.12

Step-by-step explanation:

Simplify the second expression and compare with the first one:

- 3.2(4x - 2.1) + 2.4 = - 12.8x + 3.2*2.1 + 2.4 = - 12.8x + 6.72 + 2.4 = - 12.8x + 9.12

Comparing with the first expression the value of b is:

b = 9.12

PLEASE HELP!!! How much blueberry pie will each person get if 4 people share one half of the pie equally?

Answers

Answer:

Each person gets one eighth of the pie.

Step-by-step explanation:

1/2 pie divided by 4.

1/2 / 4 = 1/2 / 4/1 = 1/2 × 1/4 = 1/8

Answer: Each person gets one eighth of the pie.

Half of a pie already is 1/2 then split that into 4 so it would be an eighth being served equally amongst them

Michael drives 18 miles in 12 minutes. If he drove three hours in total at the same rate, how far did he go?

Answers

Answer:

270 miles

Step-by-step explanation:

set up as proportion and cross multiply to solve. additionally, i represented 3 hours as 180 minutes

18 miles/12 minutes = x/180 minutes

x = 270

therefore, he went 270 miles

Help plz I’ll mark brainlist

Answers

If the scale were 1:63,360, for instance, then 1 inch on the map would represent 63,360 inches or 1 mile on the ground (63,360 inches divided by 12 inches = 5,280 feet or 1 mile).

help me solve this please

Answers

Answer:

By angle sum property

[tex](x + 22) + 60 + 58 = 180 \\ x + 140 = 180 \\ x = 40[/tex]

hope it helps you<3

Answer:

58+22+X+60=180°

x=180°-140°

x=40°

In the data set below, what is the mean absolute deviation?
8 4 7
8
5
If the answer is a decimal, round it to the nearest tenth.
mean absolute deviation (MAD):
Submit

Answers

Add the numbers and divide by 5 to get a mean of 6.4

8 - 6.4 = 1.6

4 - 6.4 = -2.4

7 - 6.4 = 0.6

8 - 6.4 = 1.6

5 - 6.4 = -1.4

Add the absolute value of each: 1.6 + 2.4 + 0.6 + 1.6 + 1.4 = 7.6

Divide by 5 = 1.52

1.5

A bag has 4 yellow marbles and 16 red marbles. Half of the red marbles are made of glass. A marble is selected at random from the bag. What is the probability
that it is a red, glass marble?
Write your answer as a fraction in simplest form.

Answers

Step-by-step explanation:

Hi. Good evening. Hope you're having a great time?

I hope my answer helps you. You can confront me if there is a misunderstanding.

Good night.

She's going to bake 12 batches of cookies. Each batch requires 1/8 cup of sugar. How many cups of sugar will grandma need for all 12 batches?

Answers

1.5 cups of sugar

1/8 cup PER batch * 12 batches
(1/8)*12 = 1.5 cups

What is 2 ÷
1
6
?

StartFraction 1 Over 12 EndFraction
2
6
12

Answers

Answer:B) 24D) 48Step-by-step explanation:Given:Two fractionsTo find:Number that can be chosen as Common denominator such that numerator is also a whole number ?Solution:Common denominatorfor two fractions and is chosen asLCM or multiple of LCMof (q, s).ORCommon denominator for two fractions is chosen as the Least Common Multiple or multiple of LCM of denominators of the two fractions.

1. y=900(1.27)^x

what is the initial value?

growth or decay?

what is the percent of change?

Answers

Answer:

The initial value is 900

It is experiencing exponential growth by 27%

Step-by-step explanation:

Exponential functions are in the form [tex]y=a(b)^x[/tex], where a is the initial value, b is the multiplier, and x is the input, such as how many years past a certain date.

Exponential growth is when the multiplier is above 1.00, or above 100%, because b is determined by 1 + r if you have exponential growth, or 1 - r if you have exponential decay. You will never use negatives with exponential decay.

A computer is on sale and is marked down 30% off regular price. After 13% tax, you pay $355.95. Calculate the regular price of the computer.

Answers

Answer:

you need to use the before change and after method

How do you solve this problem?

Answers

Answer: I don’t understand where the problem is? Can u show your whole paper so I can have a better understanding ?

Step-by-step explanation:

Find the perimeter of the figure to the nearest hundredth.

Answers

analyze data in picture

a 5*7 parallelogram and a half circle with a diameter of 5

5+7+7+5pi

is around

34.71

The campers in cabin d walked 1/6
of the way to silver stream how many miles did they walk

Answers

Answer:

but what is the question

Please show work thank you math experts

Answers

Answer:

1. 35 - 176 = -141

2. 0.55 × 1.79 = 0.9845

3. 11.38 × 5.46 = 62.1348

Hope it helps and have a great day! =D

~sunshine~

Rewrite 32 +68= 100 using the Commutative Law of Addition

Answers

68 + 32 = 100 or 32 + 68 = 68 + 32

Can I get some help? I'll give lots of points

Answers

Try this option (all the details are in the attachment).

Question
Find the area of the figure.

Answers

Answer:

Step-by-step explanation:

If you count the squares, the answer is 25

What is 12 x 11 i need this now

Answers

Answer:

bru its 132

Step-by-step explanation:

Answer:

that is 132

Step-by-step explanation:

12 over 11 then multiply

Jorge paid $9 for a book that was originally $12. What was the % discount for the book

Answers

Answer:

25%

Step-by-step explanation:

12=100%

3=25%

9=75%

What are the coordinates of the point on the directed line segment from (−1,4) to (8,−8) that partitions the segment into a ratio of 2 to 1?

Answers

Answer:

777

Step-by-step explanation:

was good double d I like McDonalds big Macs please give branilest and I really appreciate how the volunteers have done an amazing goob on big Mac for. the best taste on planet earth and it taste soooo good that I could take it to the moooon

Unit 8: Polygons And Quadrilaterals Homework 1: Angles Of Polygons (2024)

FAQs

How do you solve polygons and angles? ›

The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides. The sum of exterior angles of a polygon is 360°. The formula for calculating the size of an exterior angle is: exterior angle of a polygon = 360 ÷ number of sides.

How do you derive the sum of the interior angles of a polygon? ›

The sum of all interior angles of a regular polygon is calculated by the formula S=(n-2) × 180°, where 'n' is the number of sides of a polygon. For example, to find the sum of interior angles of a pentagon, we will substitute the value of 'n' in the formula: S=(n-2) × 180°; in this case, n = 5.

Know More ›

What is the interior angle of a 7 sided polygon? ›

For regular heptagon, the measure of the interior angle is about 128.57 degrees. The measure of the central angle of a regular heptagon is approximately 51.43 degrees. The number of diagonals in a heptagon is 14.

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What is the polygon formula? ›

Polygon Formula

The important polygon formulas are: The sum of interior angles of a polygon with “n” sides =180°(n-2) Number of diagonals of a “n-sided” polygon = [n(n-3)]/2.

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How to calculate an angle? ›

Use the sine function if you know the length of the opposite side and the hypotenuse. Plug your values into the equation: sine (x) = opposite ÷ hypotenuse. Say that the length of the opposite side is 5 and the length of the hypotenuse is 10. Divide 5 by 10, which is equal to 0.5.

Learn More Now ›

How to find the sum of angles? ›

To find the interior angle sum of a polygon, we can use a formula: interior angle sum = (n - 2) x 180°, where n is the number of sides. For example, a pentagon has 5 sides, so its interior angle sum is (5 - 2) x 180° = 3 x 180° = 540°. Created by Sal Khan.

What is the formula for finding all interior angles of a polygon? ›

A regular polygon is a flat shape whose sides are all equal and whose angles are all equal. The formula for finding the sum of the measure of the interior angles is (n - 2) * 180. To find the measure of one interior angle, we take that formula and divide by the number of sides n: (n - 2) * 180 / n.

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What is the formula for the sum of exterior angles of a polygon? ›

Ans : The sum of any regular polygon's or any polygon's exterior angles is 360°. Ans : The sum of a triangle's exterior angles is 360°. Ans : The following equation is used to determine the scale of the outside angular position of a regular polygon: 360°/n, where 'n' is the number of polygon sides.

Keep Reading ›

What is the angle sum property of a polygon? ›

The angle sum property formula for any polygon is expressed as, S = (n − 2) × 180°, where 'n' represents the number of sides in the polygon. This property of a polygon states that the sum of the interior angles in a polygon can be found with the help of the number of triangles that can be formed inside it.

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What is the sum of the exterior angles of a polygon with 7 sides? ›

If a polygon has 7 sides, then the sum of the measures of the exterior angles of the polygon is 360°.

What polygon has 7 sides 7 angles and 7 vertices? ›

Properties of Heptagon

It has seven sides, seven angles, and seven vertices. Sum of interior angles of a heptagon is 900°.

Find Out More ›

How do you find the angle between polygons? ›

What is Meant by Interior Angles of Polygon?

Note down the number of sides “n.”
To find the interior angles of a polygon, use the formula, Sum of interior angles = (n-2)×180°
To find each interior angle of a polygon, then use the general formula, ...
Substitute the given side value in the formula to get the solution.

Get More Info ›

What is the formula for calculating the number of degrees in a polygon? ›

The sum of the interior angles in a regular polygon is given by the formula 180(n – 2), where n is the number of sides in the polygon. An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees.

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How to find two missing angles in a polygon? ›

Step 1: Find the sum of the interior angle measures using the formula S = 180 ( n − 2 ) , where is the number of sides of the polygon. Step 2: Set up an equation by adding all the angle measures in the polygon and setting it equal to the result from step 1. Step 3: Solve for the missing angle.