5.2 Exterior Angles of a Polygon Investigation (Is there an Exterior Angle Sum?
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5.2 Exterior Angles of a Polygon Investigation (Is there an Exterior Angle Sum?
Step 1: Draw a large polygon. Extend its sides to form a set of exterior angles
Step 2: Measure all the interior angles of the polygon except one. Use the Polygon Sum Conjecture to calculate the measure of the remaining interior angles. Check your answer using your protector.
Step 3: Use the Linear Pair Conjecture to calculate the measure of each exterior angles
Step 4: Calculate the sum of the measure of the exterior angles. Share your results with your group members.
Step 5: Repeat steps 1-4 with different kinds of polygons, or share results with other groups. Make a table to keep track of the number of sides and the sum of the exterior angle measure for each kind of polygon. Find a formula for the sum of the measure of a polygon's exterior angles.
4 5 6 7
360 360 360 360
Exterior Angle Sum Conjecture
For any polygon, the sum of the measure of a set of exterior angles is equal to 360 degrees
Step 6: Study the software construction above. Explain how it demonstrate the Exterior Angle Sum
Conjecture
The software construction above demonstrates the Exterior Angle Sum Conjecture because the figure above is a 5 sided figure or otherwise known as a pentagon. In reference to the Polygon Sum Conjecture, it is 540 degrees which would mean the interior angles would have to sum to 540, and according to the Exterior Angle Sum Conjecture, the exterior angles will sum to 360.
Step 7: Using the Polygon Sum Conjecture, write a formula for the measure each interior angle in an equiangular polygon
A formula for the measure of each interior angle in an equiangular polygon is (n-2) 180/n
Step 8: Using the Exterior Angle Sum Conjecture, write the formula for the measure of each exterior angle in an equiangular polygon
The formula of each exterior angle in an equiangular polygon is 360/n
Step 9: Using your results from Step 8, you can write the formula for an interior angle of an equiangular polygon a different way. How do you find the measure of an interior angle if you know the measure of its exterior angle? Complete the next conjecture.
Another way to find the measure of an interior angle if you know the measure of its exterior angle is 180(360/n)
Equiangular Polygon Conjecture
You can find the measure of each interior angle of an equiangular n-gon by using either of these formulas: (n-2) 180/n or 180(360/n)