Triangles, Angles, and Diagonals in Polygons

This lesson covers the concepts of diagonals, interior angles, and exterior angles in polygons. It begins with an explanation of how to draw diagonals from a vertex in a regular hexagon, followed by calculating the sum and measure of interior angles in both hexagons and quadrilaterals. The lesson concludes with a discussion on the measure of exterior angles in a regular hexagon.

How many diagonals can be drawn from one vertex of a regular hexagon?

• 3

• 2

• 5

• 4

What is a diagonal in the context of polygons?

• A line segment connecting non-adjacent vertices

• A line segment connecting the center to a vertex

• A line segment connecting two midpoints

• A line segment connecting adjacent vertices

In a regular hexagon, how does the number of sides relate to the number of diagonals from one vertex?

• Diagonals are half the number of sides

• They are equal

• Diagonals are two less than the number of sides

• Diagonals are double the number of sides

How many triangles can a hexagon be divided into using diagonals from one vertex?

• 2

• 3

• 4

• 5

What is the sum of all interior angles in a regular hexagon?

• 900 degrees

• 720 degrees

• 540 degrees

• 360 degrees

What is the measure of each interior angle in a regular hexagon?

• 120 degrees

• 110 degrees

• 100 degrees

• 90 degrees

How many triangles are formed inside a quadrilateral when one diagonal is drawn?

• 1

• 2

• 3

• 4

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

• 450 degrees

• 360 degrees

• 270 degrees

• 180 degrees

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

• 270 degrees

• 90 degrees

• 180 degrees

• 360 degrees

What is the formula to calculate the sum of interior angles of a polygon with n sides?

• (n+2) * 180

• n * 360

• n * 180

• (n-2) * 180