Answer:
Part 1) The measure of the remaining angle is ![60\°](https://tex.z-dn.net/?f=60%5C%C2%B0)
Part 2) Is a 10 sided polygon (decagon)
Part 3) Yes, is possible for a triangle to have angles measures of 1°, 2° and 177°
Step-by-step explanation:
Part 1)
we know that
The sum of the measures of the interior angles of a polygon is equal to the formula
![S=(n-2)180\°](https://tex.z-dn.net/?f=S%3D%28n-2%29180%5C%C2%B0)
where
n is the number of sides of polygon
In this problem we have a hexagon
so
n=6 sides
Substitute
![S=(6-2)180\°=720\°](https://tex.z-dn.net/?f=S%3D%286-2%29180%5C%C2%B0%3D720%5C%C2%B0)
Let
x-----> the measure of remaining angle of the hexagon
![6*(110\°)+x\°=720\°](https://tex.z-dn.net/?f=6%2A%28110%5C%C2%B0%29%2Bx%5C%C2%B0%3D720%5C%C2%B0)
![x=720\°-660\°=60\°](https://tex.z-dn.net/?f=x%3D720%5C%C2%B0-660%5C%C2%B0%3D60%5C%C2%B0)
Part 2) The sum of the measures of the interior angles of a polygon is
. What kind of polygon is it?
we know that
The sum of the measures of the interior angles of a polygon is equal to the formula
![S=(n-2)180\°](https://tex.z-dn.net/?f=S%3D%28n-2%29180%5C%C2%B0)
where
n is the number of sides of polygon
In this problem we have
![S=1440\°](https://tex.z-dn.net/?f=S%3D1440%5C%C2%B0)
substitute in the formula and solve for n
![1440\°=(n-2)180\°](https://tex.z-dn.net/?f=1440%5C%C2%B0%3D%28n-2%29180%5C%C2%B0)
![n=(1440\°/180\°)+2=10\ sides](https://tex.z-dn.net/?f=n%3D%281440%5C%C2%B0%2F180%5C%C2%B0%29%2B2%3D10%5C%20sides)
therefore
Is a 10 sided polygon (decagon)
Part 3) Is it possible for a triangle to have angles measures of 1°, 2° and 177° ?
we know that
In any triangle the sum of the measures of the interior angles must be equal to 180 degrees
In this problem we have
1°+ 2°+ 177°=180°
therefore
Yes, is possible for a triangle to have angles measures of 1°, 2° and 177°