Understanding Diagonals in Polygons

This video tutorial explains how to determine the number of diagonals in various polygons using a specific formula. It covers examples of triangles, quadrilaterals, pentagons, hexagons, heptagons, and octagons, demonstrating the application of the formula. The video also includes an example problem involving a polygon with 35 diagonals, leading to the identification of a decagon. Additionally, it discusses the sum of interior angles and the measure of each interior and exterior angle in a decagon.

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

• d = n(n+2)/2

• d = n(n-2)/2

• d = n(n+3)/2

• d = n(n-3)/2

How many diagonals does a quadrilateral have?

• 2

• 4

• 1

• 3

For a pentagon, how many diagonals can be drawn?

• 3

• 4

• 5

• 6

What is the number of diagonals in a hexagon?

• 8

• 6

• 9

• 7

How many diagonals are there in a heptagon?

• 10

• 12

• 16

• 14

Calculate the number of diagonals in an octagon.

• 21

• 20

• 18

• 19

A polygon with 35 diagonals is known as a?

• Nonagon

• Undecagon

• Decagon

• Dodecagon

What is the sum of the interior angles of a decagon?

• 1440 degrees

• 1260 degrees

• 1620 degrees

• 1080 degrees

What is the measure of each interior angle in a decagon?

• 156 degrees

• 144 degrees

• 132 degrees

• 120 degrees

How can you calculate the measure of an exterior angle in a decagon?

• 180/n

• 180/(n-2)

• 360/(n-2)

• 360/n