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Classifying Polygons and Finding Interior Angles

Learn how to classify polygons and find the sum of their interior angles. Practice different examples and solve standardized test questions.

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Classifying Polygons and Finding Interior Angles

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 11–4) Then/Now New Vocabulary Example 1: Classify Polygons Key Concept: Interior Angles of a Polygon Example 2: Standardized Test Example Example 3: Real-World Example: Measure of One Interior Angle Example 4: Find Tessellations Lesson Menu

  3. Find the value of x. A. 128 B. 126 C. 124 D. 122 5-Minute Check 1

  4. Find the value of x. A. 80 B. 60 C. 40 D. 20 5-Minute Check 2

  5. Classify the quadrilateral. A. cube B. parallelogram C. rhombus D. quadrilateral 5-Minute Check 3

  6. Classify the quadrilateral. A. square B. parallelogram C. rhombus D. quadrilateral 5-Minute Check 4

  7. Which statement best describes a trapezoid? A. a parallelogram with exactly one pair of parallel sides B. a quadrilateral with exactly one pair of parallel sides C. a parallelogram with at least two congruent sides D. a quadrilateral with at least two congruent sides 5-Minute Check 5

  8. You have already classified quadrilaterals. (Lesson 11–4) • Classify polygons. • Determine the sum of the measures of the interior angles of a polygon. Then/Now

  9. polygon • diagonal • interior angle • regular polygon • tessellation Vocabulary

  10. Classify Polygons Determine whether the figure is a polygon. If it is, classify the polygon. If it is not a polygon, explain why. The figure has 5 sides that only intersect at their endpoints. Answer: It is a pentagon. Example 1

  11. Classify the polygon. A. pentagon B. hexagon C. heptagon D. octagon Example 1

  12. Concept

  13. Find the sum of the measures of the interior angles of a heptagon. • 1260° • B. 1080° • C. 900° • D. 1620° Read the Test Item The sum of the measures of the interior angles is (n – 2)180. Since a heptagon has 7 sides, n = 7. Example 2

  14. Solve the Test Item (n – 2)180 = (7 – 2)180 Replace n with 7. = 5 ● 180 Simplify. = 900 Multiply. The sum of the measures of the interior angles of a heptagon is 900°. Answer: The answer is C. Example 2

  15. What is the sum of the interior angles of an octagon? A. 540° B. 720° C. 900° D. 1080° Example 2 CYP

  16. Measure of One Interior Angle TRAFFIC SIGNSA stop sign is a regular octagon. What is the measure of one interior angle in a stop sign? Step 1 Find the sum of the measures of the angles. An octagon has 8 sides. Therefore, n = 8. (n – 2)180 = (8 – 2)180 Replace n with 8. = 6(180) or 1080 Simplify. The sum of the measures of the interior angles is 1080°. Example 3

  17. Measure of One Interior Angle Step 2 Divide the sum by 8 to find the measure of one angle. 1080 ÷ 8 = 135 Answer: So, the measure of one interior angle in a stop sign is 135°. Example 3

  18. PICNIC TABLE A picnic table in the park is a regular hexagon. What is the measure of one interior angle in the picnic table? A. 720° B. 128.57° C. 120° D. 108° Example 3 CYP

  19. Divide each side by 144. Find Tessellations Determine whether or not a tessellation can be created using only regular decagons. If not, explain. The measure of each interior angle of a regular decagon is 144°. The sum of the measures of the angles where the vertices meet must be 360°. So, solve 144°n = 360. 144n = 360 Write the equation. Example 4

  20. Find Tessellations n = 2.5 Simplify. Answer: Since 360 is not evenly divisible by 144, it cannot be used to make a tessellation. Example 4

  21. Which regular polygon cannot be used to create a tessellation? A. hexagon B. pentagon C. quadrilateral D. triangle Example 4 CYP

  22. End of the Lesson

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