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Sum of Interior Angles in Polygons: Lesson and Examples

Learn how to find the sum of interior angles in polygons with clear explanations and real-world examples. Master polygon classification and angle measures.

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Sum of Interior Angles in Polygons: Lesson and Examples

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  1. Lesson Menu Main Idea and New Vocabulary NGSSS Example 1: Classify Polygons Key Concept: Interior Angle Sum of a Polygon Example 2: Sum of Interior Angle Measures Example 3: Real-World Example Five-Minute Check

  2. Find the sum of the angle measures of a polygon and the measure of an interior angle of a regular polygon. • polygon • interior angle • equiangular • regular polygon Main Idea/Vocabulary

  3. MA.8.G.2.3Demonstrate thatthe sum of the angles in a triangle is 180-degrees and apply this fact to find unknown measure of angles, and the sum of angles in polygons. NGSSS

  4. Classify Polygons Determine whether the figure is a polygon. If it is, classify the polygon. If it is not a polygon, explain why. Answer: It is not a polygon because it has a curved side. Example 1

  5. Determine whether the figure is a polygon. If it is, classify the polygon. If it is not a polygon, explain why. A. yes; pentagon B. yes; hexagon C. yes; heptagon D.No; the segments do not intersect at their endpoints. Example 1 CYP

  6. Key Concept 3

  7. Sum of Interior Angle Measures ALGEBRA Find the sum of the measures of the interior angles of a 13-gon. S = (n– 2)180 Write an equation. S = (13– 2)180 A 13-gon has 13 sides. Replace n with 13. S = (11)180 or 1,980 Simplify. Answer: The sum of the measures of the interior angles of a 13-gon is 1,980°. Example 2

  8. ALGEBRA Find the sum of the measures of the interior angles of an 18-gon. A. 160° B. 2,880° C. 3,060° D. 3,240° Example 2 CYP

  9. DESIGN A designer is creating a new logo for a bank. The logo consists of a regular pentagon surrounded by isosceles triangles. Find the measure of an interior angle of a regular pentagon. Example 3

  10. Step 1Find the sum of the measures of the angles. S = (n– 2)180 Write an equation. S = (5– 2)180 Replace n with 6. S = (3)180 or 540 Simplify. The sum of the measures of the interior anglesis 540°. Example 3

  11. Step 2Divide 540 by 5, the number of interior angles, to find the measure of one interior angle. 540 ÷ 5 = 108 Answer: The measure of one interior angle of a regular pentagon is 108°. Example 3

  12. ART An artist is creating a sculpture that is made up of regular decagons. Find the measure of an interior angle of a regular decagon. A. 144° B. 225° C. 1,440° D. 1,800° Example 3 CYP

  13. Find the sum of the measures of the interior angles of a hexagon. A. 120° B. 360° C. 720° D. 1,080° Five Minute Check 1

  14. Find the sum of the measures of the interior angles of a nonagon. A. 140° B. 1,080° C. 1,260° D. 1,620° Five Minute Check 2

  15. Find the measure of one interior angle in a regular octagon. Round to the nearest tenth if necessary. A. 120° B. 135° C. 180° D. 1,080° Five Minute Check 3

  16. Find the measure of one interior angle in a regular 14-gon. Round to the nearest tenth if necessary. A. 154.3° B. 180° C. 2,160° D. 2,520° Five Minute Check 4

  17. Find the measure of one interior angle in a regular 56-gon. Round to the nearest tenth if necessary. A. 173.6° B. 176.8° C. 186.7° D. 9,720° Five Minute Check 5

  18. The following statements are true about triangle XYZ.• The measure of each angle is evenly divisible by 20.• mX is greater than mZ. • mZ is greater than mY.• mY + mZ = mX.What are the angle measures of triangle XYZ? A.mX = 120°, mY = 20°, mZ = 40° B.mX = 120°, mY = 30°, mZ = 30° C.mX = 130°, mY = 20°, mZ = 30° D.mX = 110°, mY = 50°, mZ = 20° Five Minute Check 6

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