Secondary 2
Chapter 7
7.4/7.5 - Interior and Exterior Angles of Polygons
An interior angle of a polygon faces the inside of a polygon and is formed by consecutive sides of the
polygon.
Example 1: Find Interior Angle Measures in Polygons.
Polygon
Sketch
# Sides
# Triangles
Sum of the measures of
the interior angles.
Triangle
Quadrilateral
Pentagon
Hexagon
n-gon
1. If a polygon has 100 sides, how many triangles are formed by drawing all possible diagonals from
one vertex? Explain your reasoning.
2. What is the sum of all the interior angle measures of a 100-sided polygon? Explain your reasoning.
3. Use the formula to calculate the sum of all the interior angle measures of a polygon with 32 sides.
4. If the sum of all the interior angle measures of a polygon is 9540°, how many sides does the polygon
have? Explain your reasoning.
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Secondary 2
Chapter 7
5. Use the formula developed on the previous page to calculate the sum of all the interior angle
measures of a decagon.
6. Calculate each interior angle measure of a decagon if each interior angle is congruent. How did you
calculate your answer?
7. Complete the table.
8. If a regular polygon has n sides, write a formula to calculate the measure of each interior angle.
9. Use the formula to calculate each interior angle measure of a regular 100-sided polygon.
10. If each interior angle measure of a regular polygon is equal to 150°, determine the number of sides.
How did you calculate your answer?
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Secondary 2
Chapter 7
An exterior angle of a polygon is formed adjacent to each interior angle by extending one side of each
vertex of the polygon as shown in the triangle. Each interior angle of a polygon can be paired with an
exterior angle.
Example 2: Use the formula for the sum of interior angle measures of a polygon and the Linear Pair
Postulate to calculate the sum of the exterior angle measures of a triangle.
Let’s explore the sum of the exterior angle measures of other polygons.
1. Calculate the sum of the exterior angle measures of a quadrilateral by completing each step.
a. Draw a quadrilateral and extend each side to locate an exterior angle at each vertex.
b. Use the formula for the sum of interior angle measures of a polygon and the Linear Pair
Postulate to calculate the sum of the exterior angle measures of a quadrilateral.
The sum of the measures of the exterior angles will always equal ____________.
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Secondary 2
Chapter 7
2. Complete the table. Look for a pattern.
3. When you calculated the measure of each exterior angle in the 15-sided regular polygon, did
you need to know anything about the measure of each interior angle? Explain your reasoning.
4.
If a regular polygon has 100 sides, calculate the measure of each exterior angle. Explain how
you calculated your answer.
5. What is the measure of each exterior angle of an n-sided regular polygon?
6.
If the measure of each exterior angle of a regular polygon is 18°, how many sides does the
polygon have? Explain how you calculated your answer.
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