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
Calculate the paychecks of the following people. Select the total hours and paycheck.
Answers
Answer:
If the numbers under the days of the week are the hours worked then the answers are Sue-40,$6.75,$270 Jerry-30,$5.15,154.5 Sam-38.75,$8.75,339 Step-by-step explanation:
Just add up the number of hours worked and multiply by the rate.
If a tree casts a 45-foot shadow at the same time that a 6-foot tall man casts a 7.5-foot shadow, find the height of the tree.
1 ft
36 ft
45 ft
56.25 ft
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Answer:
36 feet
Step-by-step explanation:
I believe this is the answer
CAN SOMEONE PLEASE HELP ME??!!
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Answer:
Step-by-step explanation:its ratxrat
...
The zeros of the divisor,
x-3=0,x=3
f(3)=4(3)²-3-3=30
The remainder is 30
expand the number 0.398
Answers
Answer:
00.398
Step-by-step explanation:
Answer:
Do you mean in expanded form? If so it's 0.3+0.09+0.008 I believe.
Nikki drew a rectangle with a perimeter of 18 units on a coordinate grid. Two of the vertices were (4, –3) and (–1, –3). What could be the coordinates of the other two vertices of the rectangle?
A. (4, 12) and (–1, 12)
B. (–1, 1) and (4, 1)
C. (4, 6) and (–1, 6)
D. (4, 7) and (–1, 7)
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Step-by-step explanation:
I have read about this in my class
Answer:
ITS a.
Step-by-step explanation:
Please choose all linear functions with slope that is greater than jamals linear function.
Answers
Answer:
a b
Step-by-step explanation:
What should the following equation be multiplied by in order to eliminate the fractions? x/3+x/6=11/9
Answers
Answer:
Multiply by 18
Step-by-step explanation:
Given
[tex]\frac{x}{3} + \frac{x}{6} = \frac{11}{9}[/tex]
Required
Eliminate the fraction
To eliminate the fraction, we first determine the LCM of the denominators (3, 6 and 9)
This is show below:
List out the multiplies of 3, 6 and 9
[tex]3 = 3,6,9,12,15,18,21,24,27,30...[/tex]
[tex]6 = 6,12,18,24,30...[/tex]
[tex]9 = 9,18,27...[/tex]
The least common multiple is 18.
Hence, when both sides of the equation is multiplied by 18, the fraction is eliminated;
See proof
[tex]18 * (\frac{x}{3} + \frac{x}{6}) = \frac{11}{9} * 18[/tex]
[tex]\frac{18x}{3} + \frac{18x}{6} = \frac{11*18}{9}[/tex]
[tex]6x + 3x = 11 * 2[/tex]
[tex]6x + 3x = 22[/tex]
The fraction is eliminated
Find the coordinates of the midpoint of a segment with endpoints A(-3,7) and B(8,-2)
Answers
Answer:
the midpoint is (2.5, 2.5)
11. In a swimming race, Yvonne swam 0.18 mile.
David swam 4 times as far as Yvonne. How far
did David swim?
(A) 2.2 miles
B
0.22 mile
C.7.2 miles
D
0.72 mile
Answers
Answer: D= 0.72
Step-by-step explanation: Because 0.18 times 4 is 0.72 miles.
Answer:
D. 0.72 miles
Step-by-step explanation:
Since David swam 4 times as far is Yvonne, he swam 4 times more than 0.18. 0.18 times 4 is 0.72. If you want/need to do it in your head, just imagine 0.18 as 18, and that multiplied by 4 is 72. then move the decimal point back over before the 7, to get your answer.
Two of the other choices are clearly wrong because the actual answer is way less than the other choices (except for B). One way to quickly figure out which two (or sometimes three) are wrong is by rounding 0.18 up to 0.2. You can try this quickly because 0.2 is barely bigger than 0.18, and 0.2 is easy to multiply by 4. The answer you would get from multiplying 0.2 is not exactly correct, but gives you a general idea.
Use numerals instead of words.
The Smiths are sending out a batch of holiday cards. Emily signed 2/5 of the cards. Then Josh signed 1/9 of the remaining cards. Tatiana signed 20% of what Josh had left.
If there were 75 cards in all, how many cards are left to be signed?
There are
cards yet to be signed.
Answers
Answer:
25 because is the steep between card
Answer:
32
I hope this helps
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:
3.) Jimena used her calculator to divide 2 by 13.
The calculator screen shows the number: 0.1538461.
Round Jimena's answer to the nearest tenth. =
Answers
Answer: 0.2
Step-by-step explanation:
What are the missing angles?
Answers
2. 34
3. 95
4. 38
5. 47
6. 74
7. 59
I hope this helps!!
Find the slope between the following points (2,5) and (-3,-9)
Answers
Answer: 14/5
Step-by-step explanation: Use Algebra calculator on math papá.com
Answer:
[tex]m=\frac{14}{5}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (2, 5)
Point (-3, -9)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
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Answers
Answer:
x int= -4 y int= 1
Step-by-step explanation:
intercepts refer to the place on the each axis where the line passes through
A line has a slope of 6 and includes the points (n,1) and (8,5). What is the value of n?
Answers
Answer:
The value of n:
[tex]n=\frac{22}{3}[/tex]Step-by-step explanation:
Given that the line has slope 6.
i.e. m = 6
The line includes the points
(n, 1)(8, 5)Using the formula to find the slope of the points
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(n,\:1\right),\:\left(x_2,\:y_2\right)=\left(8,\:5\right)[/tex]
[tex]m=\frac{4}{8-n}[/tex]
as
m = 6
substituting m = 6
[tex]6=\frac{4}{8-n}[/tex]
[tex]6\left(8-n\right)=4[/tex]
Divide both sides by 6
[tex]\frac{6\left(8-n\right)}{6}=\frac{4}{6}[/tex]
[tex]8-n=\frac{2}{3}[/tex]
subtract 8 from both sides
[tex]8-n-8=\frac{2}{3}-8[/tex]
simplify
[tex]-n=-\frac{22}{3}[/tex]
Divide both sides by -1
[tex]\frac{-n}{-1}=\frac{-\frac{22}{3}}{-1}[/tex]
[tex]n=\frac{22}{3}[/tex]
Therefore, the value of n:
[tex]n=\frac{22}{3}[/tex]Question
20 pts
There are 600 6th grade students who attend Falcon Cove Middle School. 17% of them
believe that Mr. Too Much should be fired for being the silliest teacher they have ever known.
How many 6th graders at Falcon Cove believe Mr. Too Much should be fired?
6th graders at Falcon Cove believe Mr. Too Much should be fired.
Question 2
20 pt
Answers
Answer:
u can ask the tutor and he or she will help u in real time and explain
007
0.3
X
How to multiply .007 by 0.3?
Answers
Answer:
0.0021
Step-by-step explanation:
0.007 x 0.3= 0.0021
X 0. 3
—————
Multiple
7x3 since the other are 0
You get 21 then add the 0
Your answer will be 0.0021
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Answers
Answer:
I think the answer is 53.75 inches
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16+(14-6)x3-62-6
O 18
O None of the other answers are correct
O 78
0 34
O 12
Answers
getting bored.Is there anyone???
Answers
Answer:
yes very much so
Step-by-step explanation:
yes I don't know why but I am really and truly
Answer:
WOW yRRRRRR
Step-by-step explanation:
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Answers
Answer:
Bob only has 40 dollars but he wants to buy a membership at the gym. It cost 8 dollars per month to receive a gym card. Bob went to the Gym in person so they gave him a 5 dollar off coupon. How many months can Bob buy?
Step-by-step explanation:
Answer:
eight and a variable subtracted by five equals forty
Step-by-step explanation:
Is there anyone here who does Calvert or Odessy?
I was quite behind on my assignments, and, somehow, I go to catch up and they've been completed or something. It says I'm 100% on pace, and I know for a fact that I wasn't. What happened?
Answers
what happen is there is a glitch probably
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PLEASE HELP WILL MARK BRAINLEIST
Answers
Answer:
The second one
Step-by-step explanation:
because 1•4=4 and 2•2=4
Please help me with this
Answers
Answer:
6.7
Step-by-step explanation:
5x+2(x+6)
A.7x+6
B.7x^2+12
C.7x+12
D.7x(x+6)
Answers
What is 3(2+q)+15 simplified
Answers
Answer:
The Answer should be....
3q + 21
In a certain Algebra 2 class of 24 students, 9 of them play basketball and 13 of them
play baseball. There are 2 students who play both sports. What is the probability that
a student chosen randomly from the class plays basketball or baseball?
Answers
The probability that a student who is chosen randomly from the class who plays basketball or baseball is 11/24.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Given that In a certain algebra 2 class of 24 students, 9 of them play basketball and 13 of them play baseball. There are 2 students who play both sports.
2+5+4 =11
Expect the 13 people/students who didn't play,
Total people 24
P = 24-13=11
P = 11/24
The probability will be equal to 11/24.
To know more about probability follow
https://brainly.com/question/24756209
#SPJ1
The following histogram shows the height of basketball players what would be the best estimate of average height ?
A. 75in
B. 82in
C. 85in
D. 80in
Answers
Answer:
D
Step-by-step explanation:
Number 1
In the relation, what is the domain?
I
In the relation, what is the range?
Answers
Answer:
Step-by-step explanation:
D(x)= (-1, -1\2, 3/2, 2)
A domain is any X value in an array of ordered pairs
