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Learn it your way
A short class with Sarah and her students. The other ways are under More.
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Today, we will start by discussing what exterior angles are. Does anyone know how they differ from interior angles?
I think exterior angles are the angles outside the polygon when a side is extended.
Exactly! When you extend a side of a polygon, the angle formed outside is an exterior angle. Can anyone give an example of a polygon and say how many exterior angles it has?
A triangle has three exterior angles!
Great! And if we think about a pentagon, how many exterior angles does that have?
Five exterior angles.
Right! Now, here’s a memory aid: remember the phrase 'exterior equals 360'! This helps us remember that the total of all exterior angles of any polygon is always 360°. Can someone summarize what we discussed?
Exterior angles are outside the polygon, and their total measure is always 360°.
Now that we understand exterior angles, let’s learn how to calculate unknown angles. If I tell you the first angle is 90°, the second is 50°, and the third is 110°, how can we find the unknown fourth angle?
We can add the known angles and subtract from 360°.
Exactly! So we calculate it like this: 90° + 50° + 110° = 250°. To find the unknown angle, we do 360° - 250°.
That means the fourth angle is 110°!
Good work! Always remember this formula when calculating unknown angles. Who can summarize what we just learned?
To find an unknown exterior angle, add known angles and subtract from 360°.
For this activity, I want you each to draw a polygon on the floor with chalk. As you walk around and turn at each vertex, measure your turns. What do you observe?
When I walked around my pentagon, all the turns I made added up to 360°!
Me too! It’s the same for my hexagon.
Excellent observations! This is a clear demonstration of how the sum of exterior angles is always 360° for any polygon. Who can remind us why this is significant?
It helps us understand the shape and size of polygons, especially when calculating angles.
Exactly right! Now let’s summarize today’s lessons.
Exterior angles add up to 360°, and we can calculate any unknown angles using this rule.
When you walk around a shape, make a turn, count the degrees, it's 360° you'll learn.
Imagine walking around a park (polygon); every corner you turn adds to a full circle, which is always 360°.
EVERY POLYGON has an exterior angle sum of 360° — remember 'EPE360'.
EAP: Exterior Angles Always 360°.
Term
Exterior Angle
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Term
Sum of Exterior Angles
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The sum of the measures of the exterior angles of any polygon is always 360°.
Exterior angles of a polygon provide useful insights into the nature of interior angles and help in understanding polygon geometry. This section demonstrates that regardless of the number of sides a polygon has, the total measure of its exterior angles remains constant at 360°.
In this section, we explore the concept of exterior angles of polygons. An exterior angle is formed when you extend one side of the polygon. The section highlights that when you walk around a polygon and measure each turn you make (the exterior angle), the sum of these angles amounts to 360°. For instance, if you take a pentagon, as you walk along its edges and turn at each vertex, you will find that the cumulative measure of the turns is 360°. This relationship holds true for any polygon, regardless of the number of sides.
The section includes examples and problems prompting students to calculate unknown exterior angles using the established formula. Moreover, it emphasizes activities such as drawing polygons to physically demonstrate the concept and its universal applicability. This understanding lays the foundation for further exploration into polygon properties in geometry.
Example : Find the number of sides of a regular polygon whose each exterior angle has a measure of 60°.
Solution: Total measure of all exterior angles = 360°
Measure of each exterior angle = 60°
Therefore, the number of exterior angles = .
The polygon has 6 sides.