Answer:
Part 1) The measure of the remaining angle is [tex]60\°[/tex]
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
[tex]S=(n-2)180\°[/tex]
where
n is the number of sides of polygon
In this problem we have a hexagon
so
n=6 sides
Substitute
[tex]S=(6-2)180\°=720\°[/tex]
Let
x-----> the measure of remaining angle of the hexagon
[tex]6*(110\°)+x\°=720\°[/tex]
[tex]x=720\°-660\°=60\°[/tex]
Part 2) The sum of the measures of the interior angles of a polygon is [tex]1440\°[/tex]. 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
[tex]S=(n-2)180\°[/tex]
where
n is the number of sides of polygon
In this problem we have
[tex]S=1440\°[/tex]
substitute in the formula and solve for n
[tex]1440\°=(n-2)180\°[/tex]
[tex]n=(1440\°/180\°)+2=10\ sides[/tex]
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°
