Mathematics College

Drag and drop formal proof. Prove the Polygon Exterior Angle Sum Theorem for the enclosed triangle, that is ∠1+∠2+∠3=360°
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Drag And Drop Formal Proof. Prove The Polygon Exterior Angle Sum Theorem For The Enclosed Triangle, That

Answers

Answer 1

Answer:

The sum of all the external angles of a triangle is 360°.

Step-by-step explanation:

Let there are n sides in a polygon.

So, there are n internal angles in the polygon, let ∠i1, ∠i2, ∠i3, ..., ∠in are the measure of n internal angles of the polygon.

The measure of external angle corresponding to ∠i1,  ∠1= 180°-∠i1,

The measure of external angle corresponding to ∠i2, ∠2 = 180°-∠i2,

Similarly, the measure of external angle corresponding to ∠in, ∠n = 180°-∠in.

Now, the sum of all the external angles of the polygon,

(∠1+∠2+...+∠n)=(180°-∠i1)+(180°-∠i2)+...+(180°-∠in)

=(180°+180°+...n times)-(∠i1+∠i2+...+∠in)

=n x 180° - (∠i1+∠i2+...+∠in)

As ∠i1+∠i2+...+∠in is the sum of all the internal angles of the polygon.

So, the sum of all the external angles of the polygon =

(n x 180°) - (sum of all the internal angles of the polygon).

In the case of a triangle, n=3  and the sum of all the three internal angles, ∠i1+∠i2+∠i3 = 180°.

Therefore, the sum of all the external angles of a triangle,

∠1+∠2+∠3 =3x180°-(∠i1+∠i2+∠i3)

                 =540°=180°

                 =360°.

Hence, the sum of all the external angles of a triangle is 360°.

Related Questions


Laura can finish payroll in 3
hours. It takes Ben 5 hours
to do the same job. If they
work together, how long
should it take them?
hours

Answers

Answer:

1/2

Step-by-step explanation:

First we divide 3 and 5, which gives us 0.6, then we use the LA Hypothalamus formula which is x2, so then we substitute the x with 0.6, 0.6 multiplied by 2 is 1.2, so then we transform it to a fraction, your welcome

Answer:

15/8

Step-by-step explanation:


[tex]2 log_{2}(x) + \frac{1}{2} log_{2}(x - 1) - log_{2}( x + 3) [/tex]
solving these problem​

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I'm putting here a picture of the working out

What is the slope of the line which passes through (4,7) and (2, 3)? (5 points)
2
-2.
3
-5

Answers

Answer:

2

Step-by-step explanation:

What is the ideal number of children to have in a family? The following data represent the ideal number of children for a random sample of 900 adult Americans. ​

Answers

Answer:

4

Step-by-step explanation:

In most modern family’s they usually have 4 or 2

A map is made of a park. The scale from the park to the map is 36 mi to 9 cm. The length of Great Oaks Trail is 3 cm on this map. What is the actual length of the Great Oaks Trail?

Answers

Answer:

yes rhudurueufuurehhehduruejjdjdif

Answer:

11 miles

Step-by-step explanation:

3 centimeters is 1/3 of 9 centimeters so whatever you do to that you do the other number, so you divide 36 by 3 which is 11

Jason and his twin brother, Seth, are painting the walls in their bedroom. It took Jason 50 minutes to paint a 160-square-foot wall. It took Seth 30 minutes to paint a 120-square-foot wall. Who painted faster?

Answers

Answer:

Jason

Step-by-step explanation:

Answer:

It's Seth

Step-by-step explanation:

Find the area. Round to the nearest hundredth if necessary

Answers

add 16.7m 4 times that should be the correct answer if not sorry

What is the quotient of (x3 + 6x2 + 11x + 6) ÷ (x2 + 4x + 3)?

Answers

Answer:

=x+2

Step-by-step explanation:

x3+6x2+11x+6

x2+4x+3

=

x3+6x2+11x+6

x2+4x+3

=

(x+1)(x+2)(x+3)

(x+1)(x+3)

Answer:

a. x+2

Step-by-step explanation:

took the test

I NEED HELP !!!! A taxi driver spends $105 every week on gas for 6 weeks. What integer represents the effect of buying $105 on gas for 6 weeks on the taxi driver’s bank account, in dollars?

Answers

.Answer:

-105

Step-by-step explanation:

Given

[tex]Gas = \$105[/tex] for 6 weeks

Required

Represent this as an integer

If the driver spends $105 on his taxi then it means that the money is debited from the driver's bank account.

Debit implies negative and it is represented by a negative symbon

Hence, the integer that represents this scenario is -105

What’s the 2 numbers I need pls help

Answers

Answer:

y=-1/4x-6

Step-by-step explanation:

Y-intercept is -6 because that is where the line touches on the y-axis. For slope, pick two points and remember rise over run.

Pick (0,-6) and (4,-7) for example. Referencing the graph, from -6, count over and down until you get to (4,-7). The line represents a negative slope, so your slope is -1/4

What is 5j + 3m - 2j - j2 - 8 + 3??

Answers

Subtract 2j from 5j

3j+3m-j2-8+3

Simplify the expression

Add -8 and 3

3j+3m-j^2-5

Move 3j

3m-j^2+3j-5

Reorder 3m and -j^2

-j^2+3m+3j-5

interact if u in k12

Answers

Answer:

im in k12, hello and how are you on this fine day? :D

Step-by-step explanation:

Answer:

asdfghjkl

Step-by-step explanation:

Can someone solve this question please?
m/9=-9

Answers

Answer:

=−81

step-by-step explanation:

Multiply all terms by the same value to eliminate fraction denominators

m/9=-9

(9)m/9=9(-9)

m=9(-9)

plz help me answer my questions too go to my page

Find the ratio of 2p per gram to £2.12 per kilogram

Answers

Answer:

the answer is 1.06

Step-by-step explanation:

QUESTION 2
Solve the equation for exact solutions.
arccos x + arccos 2x = arccos
1/2

Answers

The third one is the correct answer

(x + 1)^2 -8 (x-1 +16)

Answers

Answer: x2−6x−119

Step-by-step explanation:

provided in the screenshot below

Does anyone know part B to this?!?!? I will give brainilest

Answers

Answer:

(0,7)

Step-by-step explanation:

Which is greater 0.691 or 3.5

Answers

Answer:

3.5 is greater

Step-by-step explanation:

Answer:

3.5

Step-by-step explanation:

it is known as common sense

Evaluate the expression when x = 32 and y = 2.

x over 4y

Answers

Answer:

4

Step-by-step explanation:

[tex]\frac{32}{4x2}[/tex]

[tex]\frac{32}{8}[/tex]

[tex]\frac{16}{4}[/tex]

[tex]\frac{4}{1}[/tex]

4

A line includes the points (-15, 5) and (-12, 5). What is its equation in slope-intercept form?
form

Answers

Answer:

y=5

Step-by-step explanation:

y=mx+b is slope intercept form

Please give me the correct answer ​

Answers

Last one :) djsjsjdndnwjdjnd
The Awnser is the last one

Solve the inequality​

Answers

i think it would be x< 3?

please help me pplease

Answers

Answer:

B)

Step-by-step explanation:

its b because it doesnt have to turn to slow down

1+1
2
asdlakfakljsbfklajbsfkajbsfkjbaksfjbaskfjasf

Answers

Answer:2 ufghcdthggcfghgfftg

Step-by-step explanation:

OMg Its TwO OmG ThaTs The anSwer

The population of a town is 20.000. It decreases at a rate of 9% per year. In about how many years will the population be fewer than 13,000?

Answers

4 years, just like what the other person said he is right. because 9% of population is 1800

It will take approximately four years for the population to be fewer than 13,000.

What is the rate?

A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.

The population of the town is 20.000. It decreases at a rate of 9% per year.

The population of the town decreases by 20,000 × 9% = 1,800 people per year.

To determine how many years it takes for the population to fall below 13,000, you can use the formula:

= (20,000 - 13,000) / 1,800

= 3.88 ≈ 4 years

So, it will take approximately 4 years for the population to be fewer than 13,000.

To learn more about the rate click here :

https://brainly.com/question/12786410

#SPJ6

X+23
2x-17
What is the value of x?

Answers

Answer:

a value

Step-by-step explanation:

Answer:

Simplifying

4x + -23 = 2x + 17

Reorder the terms:

-23 + 4x = 2x + 17

Reorder the terms:

-23 + 4x = 17 + 2x

Solving

-23 + 4x = 17 + 2x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2x' to each side of the equation.

-23 + 4x + -2x = 17 + 2x + -2x

Combine like terms: 4x + -2x = 2x

-23 + 2x = 17 + 2x + -2x

Combine like terms: 2x + -2x = 0

-23 + 2x = 17 + 0

-23 + 2x = 17

Add '23' to each side of the equation.

-23 + 23 + 2x = 17 + 23

Combine like terms: -23 + 23 = 0

0 + 2x = 17 + 23

2x = 17 + 23

Combine like terms: 17 + 23 = 40

2x = 40

Divide each side by '2'.

x = 20

Simplifying

x = 20

Step-by-step explanation:

What is slope of the equation? 7x -2y = -10

Answers

Answer:

m = 7/2

Step-by-step explanation:

Brainliest Please!!?!!!!

Answer:

m=7/2

Step-by-step explanation:

explain how to use the unit rate to make a table​

Answers

Answer:

to make a unit rate using a table you would take an input/output from a table and convert it into a fraction. Then you would take that fraction and simplify it. Sometimes you might have to choose a new input/output in order to make the simplification easier.

Example-

2:4

4:8

6:12

8:16

        Turn one into a fraction

4/8

       Simplify

1/2

Does anyone know how to solve this ratio?

Answers

Answer:

The answer to this question is 11:3

11. The cost of shipping a package varies directly with the weight of the package. A 5
pound package costs $3.40 to ship. What would be the price of a package that weighs
1
12
pounds?
2
TAAR
x+b
+/-
*
med

Answers

Answer:

76.16

Step-by-step explanation:

5/3.40  =  112/x:

first combine like terms, which gives you

5x  =  3.40 × 112

next multiply 3.40 by 112 (simplifying) so you get

5x  =  380.8

last you divide 380.8 by 5x getting your answer of $76.16

hope this helped! :)

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