Polygons and Diagonals

What is a diagonal in a polygon?

• A line of a polygon

• A segment of a polygon

• A segment from one vertex to another vertex of a polygon

• A segment from one side to another side of a polygon

What is the formula to find the number of diagonals in a polygon?

• $\left(n-2\right)\cdot180$

• $\left(n-2\right)\cdot\frac{180}{2}$
  

• $\frac{360}{n}$
  

• $\frac{\left(n-3\right)\cdot n}{2}$
  

In the diagonal formula, what does (n-3) represents?

• It represents the number of diagonals just from one vertex

• It represents the number of sides a polygons has

• It represent the number of sides minus 3

• It represent the number of vertices a polygon has

In the diagonal formula we dive by 2 because:

• We need to multiply the number of diagonals

• to avoid double counting diagonals

• to add more diagonals to the polygon

• to remember the formula

How many diagonals does a 9-gon have?

• 54

• 27

• 9

• 18

How many diagonals does a 80-gon have?

• 80

• 77

• 3080

• 2085

Which polygon has 90 diagonals?

• A 90-gon

• A 12-gon

• A 10-gon

• A 15-gon

Which polygon have 275 diagonals?

• A 275-gon

• A 25-gon

• A 30-gon

• none of the above

How many diagonals does a 400-gon have?

• 79400

• 400

• 200

• 79500

What is the sum of the interior angles of a 30-gon?

• 5040

• 30

• 360

• 3040