1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
aleksandr82 [10.1K]
3 years ago
10

Drag and drop formal proof. Prove the Polygon Exterior Angle Sum Theorem for the enclosed triangle, that is ∠1+∠2+∠3=360°

Mathematics
1 answer:
jasenka [17]3 years ago
5 0

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°.

You might be interested in
HELP!! WILL GIVE BRAINLIEST!!!
otez555 [7]

Answer:

David needs 7-8 short term rentals monthly to match revenue from a lease. College students need long term housing so he should lease his home.

Step-by-step explanation:

8 0
3 years ago
Equation: y = 6x<br> When x = 8.<br> What is y?
aivan3 [116]

Answer:

48

Step-by-step explanation:

y=6x

y=6(8)=48

4 0
3 years ago
Read 2 more answers
Plzz help for brainly
PolarNik [594]

Answer:first one

Step-by-step explanation:

8 0
3 years ago
In my school there are 500 students. 20% of
S_A_V [24]

Answer:

It is do not we're spectacles

5 0
2 years ago
Read 2 more answers
I need help!!!!!!!!???!!!!!!!!??
oksano4ka [1.4K]
Its 27 if you’re adding at the bottom, but I cant really tell since it’s cropped
4 0
2 years ago
Read 2 more answers
Other questions:
  • HELP! 30 pts!<br> The circle below is centered at the point (-2, -3) and has a radius of length 3.
    7·1 answer
  • What is the answer to f(0)=(x-3)'2?
    12·1 answer
  • In the function y = 10.00x + 35, y represents the cost of cabin lodging per occupant and x represents the number of occupants. H
    9·1 answer
  • 84052 in word from plz need help in my homework
    13·2 answers
  • Max is making a rectangular garden that is 5 feet less than twice it's width. If the perimeter of the garden is 80 feet, what wi
    15·1 answer
  • The diameter of letias cup is 3 inches. What is the circumference
    8·1 answer
  • Select the letter that correctly identifies the base of the prism.
    12·2 answers
  • Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol ( μ, rho, σ) for the indicat
    15·2 answers
  • it is a polynomial equation of degree two that can be written in tche form, where a,b, and c are real numbers and a =/
    10·1 answer
  • Julie is using the set {7,8,9,10,12} to solve the inequality shown
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!