F24 Exploring Polygon Angles: Triangle through Octagon
Move the vertices (corners) of this TRIANGLE anywhere you'd like. Explore!
How many sides does a triangle have?
3
What is the sum of the interior angles of a triangle?
180
What do you notice about the exterior angles of a triangle?
They are complementary
They add up to 180[math]^\circ[/math]
They are supplementary
They add up to 360[math]^{\circ}[/math]
Move the vertices (corners) of this QUADRILATERAL anywhere you'd like. Explore!
How many sides does a quadrilateral have?
4
What happened to the quadrilateral during the Slide Me exploration?
divide up into two triangles
Into how many triangles was the shape divided?
2
What is the sum of the interior angles of a quadrilateral?
360
What do you notice about the exterior angles of a quadrilateral?
They add up to 180[math]^\circ[/math]
They add up to 360[math]^{\circ}[/math]
They are supplementary
Pentagon
How many sides does a pentagon have?
5
How many triangles were created in the pentagon during the Slide Me?
3
What is the sum of the interior angles of a pentagon?
540
What do you notice about the exterior angles of a pentagon?
They are supplementary
They add up to 180[math]^\circ[/math]
They add up to 360[math]^{\circ}[/math]
Hexagon
How many sides does a hexagon have?
6
How many triangles were created in the hexagon during the Slide Me?
4
What is the sum of the interior angles of a hexagon?
720
What do you notice about the exterior angles of a hexagon?
They add up to 180[math]^\circ[/math]
They add up to 360[math]^{\circ}[/math]
They are supplementary
Heptagon
How many sides does a heptagon have?
7
How many triangles were created in the heptagon during the Slide Me?
5
What is the sum of the interior angles of a heptagon?
900
What do you notice about the exterior angles of a heptagon?
They add up to 180[math]^\circ[/math]
They add up to 360[math]^{\circ}[/math]
They are supplementary
Octagon
How many sides does an octagon have?
8
How many triangles were created in the octagon during the Slide Me?
6
What is the sum of the interior angles of a hexagon?
1080
What do you notice about the exterior angles of an octagon?
They add up to 360[math]^{\circ}[/math]
They are supplementary
They add up to 180[math]^\circ[/math]
For any n-gon, how many sides will it have?
n
For any n-gon, how many triangles will it be divided up into? Write an equation using n as the number of sides.
n-2
How many degrees in any triangle?
180
To find the sum of the interior angles of any n-gon, what equation have we just come up with?
(n-2)*180
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Information: F24 Exploring Polygon Angles: Triangle through Octagon