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

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

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:

Please give me the correct answer ​

Answers

Last one :) djsjsjdndnwjdjnd
The Awnser is the last one

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

Solve the inequality​

Answers

i think it would be x< 3?

1+1
2
asdlakfakljsbfklajbsfkajbsfkjbaksfjbaskfjasf

Answers

Answer:2 ufghcdthggcfghgfftg

Step-by-step explanation:

OMg Its TwO OmG ThaTs The anSwer

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

Answers

Answer:

the answer is 1.06

Step-by-step explanation:


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:

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

Does anyone know how to solve this ratio?

Answers

Answer:

The answer to this question is 11:3

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

Answers

The third one is the correct answer

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

Answers

Answer:

(0,7)

Step-by-step explanation:

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! :)

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

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 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:

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:


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

Answers

I'm putting here a picture of the working out

please help me pplease

Answers

Answer:

B)

Step-by-step explanation:

its b because it doesnt have to turn to slow down

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

Answers

Answer: x2−6x−119

Step-by-step explanation:

provided in the screenshot below

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

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

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 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:

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

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

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

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

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

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