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

Part 1) The measure of the remaining angle is

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

where

n is the number of sides of polygon

In this problem we have a hexagon

so

n=6 sides

Substitute

Let

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

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

where

n is the number of sides of polygon

In this problem we have

substitute in the formula and solve for n

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°

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square

{3 + i, 3 - i, 3, -1}

step-by-step explanation: