Drag and drop formal proof. Prove the Polygon Exterior Angle Sum Theorem for the enclosed triangle, that is ∠1+∠2+∠3=360°
.
Answers
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
Which is greater 0.691 or 3.5
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Answer:
3.5 is greater
Step-by-step explanation:
Answer:
3.5
Step-by-step explanation:
it is known as common sense
Does anyone know how to solve this ratio?
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Answer:
The answer to this question is 11:3
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:
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 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
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:
Does anyone know part B to this?!?!? I will give brainilest
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Answer:
(0,7)
Step-by-step explanation:
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 help me pplease
Answers
Answer:
B)
Step-by-step explanation:
its b because it doesnt have to turn to slow down
interact if u in k12
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Answer:
im in k12, hello and how are you on this fine day? :D
Step-by-step explanation:
Answer:
asdfghjkl
Step-by-step explanation:
QUESTION 2
Solve the equation for exact solutions.
arccos x + arccos 2x = arccos
1/2
Answers
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 is 5j + 3m - 2j - j2 - 8 + 3??
Answers
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
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
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! :)
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
Please give me the correct answer
Answers
Find the area. Round to the nearest hundredth if necessary
Answers
[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
1+1
2
asdlakfakljsbfklajbsfkajbsfkjbaksfjbaskfjasf
Answers
Answer:2 ufghcdthggcfghgfftg
Step-by-step explanation:
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 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
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
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
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:
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Step-by-step explanation:
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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)
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Find the ratio of 2p per gram to £2.12 per kilogram
Answers
Answer:
the answer is 1.06
Step-by-step explanation:
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?
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Answer:
Jason
Step-by-step explanation:
Answer:
It's Seth
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