Question

In a hexagon, all but one of the angles have a measure of 110. What is the measure of the remaining angle?

Answer 1

Part 1) The measure of the remaining angle is
`60\°`

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°

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\°`

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\°`

Let

x-----> the measure of remaining angle of the hexagon

`6*(110\°)+x\°=720\°`

`x=720\°-660\°=60\°`

Part 2) The sum of the measures of the interior angles of a polygon is
`1440\°`. 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\°`

where

n is the number of sides of polygon

In this problem we have

`S=1440\°`

substitute in the formula and solve for n

`1440\°=(n-2)180\°`

`n=(1440\°/180\°)+2=10\ sides`

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°