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Geometry
January 6, 2014
Polygon Interior Angles Theorem
• The sum of the measures of the interior angles of a convex polygon is given
by taking the number of the sides (n) subtracting 2 and multiplying by 180°
The interior angle sum for the figure at the left is given by:
The number of sides: n =7
Therefore, 𝑛 − 2 ∗ 180° →
7 − 2 ∗ 180° = 5 ∗ 180°
= 𝟗𝟎𝟎°
Example 1
• Find the interior angle sum for the polygon:
• 𝑛 = 10
• 𝑛 − 2 ∗ 180°
• 10 − 2 ∗ 180°
• 8 ∗ 180°
• 1440°
Interior Angles of A Quadrilateral
• The sum of the measures of the interior angles of a
quadrilateral is 360°
• 𝑛 = 4 → 𝑛 − 2 ∗ 180°
= 4 − 2 ∗ 180°
= 2 ∗ 180°
= 360°
Example 2
• Solve for 𝑥.
• 90° + 90° + 23𝑥 − 2 ° + 21𝑥 + 6 ° = 360°
• 90 + 90 − 2 + 6 ° + 23𝑥 + 21𝑥 ° = 360°
• 184° + 44𝑥° = 360°
• 44𝑥° = 360° − 184°
• 44𝑥° = 176°
• Divide by 44°  𝑥 = 4
Example 3
• Find the measure of one interior angle in the polygon.
• 𝑛=6
•
𝑛 − 2 ∗ 180°
• 4 ∗ 180°
• 720°
• We then take the sum of the interior angles and divide by 6 (the number of
angles) since the shape is a “regular” hexagon- meaning all sides and all angles
are equal.
• 720° ÷ 6 = 𝟏𝟐𝟎°
Homework
Assignment 6-1 is posted and is due on
Thursday, January 8.