Answer:
- The sum of the interior angles of the 15-gon
![=\:2340^0](https://tex.z-dn.net/?f=%3D%5C%3A2340%5E0)
- Each interior angle of the regular polygon
![=\:156^0](https://tex.z-dn.net/?f=%3D%5C%3A156%5E0)
Step-by-step explanation:
As we know that
In any convex polygon, if we may start at one vertex and draw the diagonals to all the other vertices, we would form triangles,
The number of triangles thus formed would always 2 LESS than the number of sides.
As
- The sum of measure of the angles of any triangle is 180°.
Thus,
The sum of the interior angles of the 15-gon will be:
![13\:\times\:180\:=\:2340^0](https://tex.z-dn.net/?f=13%5C%3A%5Ctimes%5C%3A180%5C%3A%3D%5C%3A2340%5E0)
Also
15-gon is regular, it means this total
is shared in equal proportion among the 15 interior angles.
And
Each interior angle of the regular polygon will be: ![\frac{2340^{0} }{15}=156^{0}](https://tex.z-dn.net/?f=%5Cfrac%7B2340%5E%7B0%7D%20%7D%7B15%7D%3D156%5E%7B0%7D)
Therefore, we conclude that:
- The sum of the interior angles of the 15-gon
![=\:2340^0](https://tex.z-dn.net/?f=%3D%5C%3A2340%5E0)
- Each interior angle of the regular polygon
![=\:156^0](https://tex.z-dn.net/?f=%3D%5C%3A156%5E0)
Keywords: regular polygon, 15-gon, triangle
Learn more about polygon from brainly.com/question/11932357
#learnwithBrainly
Answer:
Step-by-step explanation:
1. 2 square root 7
2. 6 square root 2
3. 2 square root 5
Answer:
8
Step-by-step explanation:
Considering the given value of sum of interior angles with exclusion of one to be 1070 then we can write it as
1070=180(n-2) where n is the number of sides required here.
Making n the subject of the formula then following step by step
![n-2=\frac {1070}{180}](https://tex.z-dn.net/?f=n-2%3D%5Cfrac%20%7B1070%7D%7B180%7D)
![n=\frac {1070}{180}+2\\n=7.9444444444444\approx 8](https://tex.z-dn.net/?f=n%3D%5Cfrac%20%7B1070%7D%7B180%7D%2B2%5C%5Cn%3D7.9444444444444%5Capprox%208)
Therefore, the shape is octagon and it has 8 sides.
D = 109 - 84 = 134 - 109 = 25
2nd term = 34 + 25 = 59
[] Similar
-> The triangles are similar because they were "mirrored" by the...
[] SSS
-> ... by the SSS similarity theorem, the sides are...
[] Proportional
-> ... the sides are proportional.
[] AB/AC
-> Since the sides are proportional, dividing corresponding sides will leave us with the same number
[] For the last two I think I am missing some information as I do not have any numbers and know where they got 85 from.
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather