Properties of Polygons_ Tutorial3

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School

University of South Carolina *

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A503

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Mathematics

Date

Apr 3, 2024

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pdf

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6

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2/28/24, 12:18 PM Lesson Activity: Regular Convex Polygons https://f1.app.edmentum.com/courseware-delivery/ua/125276/45610409/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV… 1/6 Lesson Activity Regular Convex Polygons This activity will help you meet these educational goals: You will explore regular convex polygons by applying the interior angle sum theorem and the relationships between interior and exterior angles. Directions Read the instructions for this self-checked activity. Type in your response to each question, and check your answers. At the end of the activity, write a brief evaluation of your work. Activity In this activity, you will apply what you've learned about the sum of the interior and exterior angles of convex polygons and regular convex polygons. Question 1 The sum of the measures of the interior angles of a convex polygon is . How many sides does the polygon have? Answer: 50 Space used (includes formatting): 9 / 15000 Hide Sample Answer
2/28/24, 12:18 PM Lesson Activity: Regular Convex Polygons https://f1.app.edmentum.com/courseware-delivery/ua/125276/45610409/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV… 2/6 The sum of the interior angles of a convex polygon is . Therefore, . Solve for The polygon has 50 sides. Question 2 An interior angle of a regular convex polygon is . How many sides does the polygon have? Answer: 15 sides Space used (includes formatting): 15 / 15000 Since the polygon is regular, all interior angles are congruent, and all exterior angles are congruent. Using the fact that an interior and exterior angle form a linear pair, solve for an exterior angle: . Solve for the number of sides: . The polygon has sides. Hide Sample Answer
2/28/24, 12:18 PM Lesson Activity: Regular Convex Polygons https://f1.app.edmentum.com/courseware-delivery/ua/125276/45610409/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV… 3/6 Question 3 Fill in the missing information in the table. Answer: Regular Polygon Interior Angle Sum One Interior Angle Exterior Angle Sum One Exterior Angle hexagon 108° 45° decagon 1800° 90° Space used (includes formatting): 1096 / 15000 Regular Polygon Interior Angle Sum One Interior Angle Exterior Angle Sum One Exterior Angle hexagon 720° 120° 360° 60° pentagon 540° 108° 360° 72° octagon 1080° 135° 360° 45° decagon 1440° 144° 360° 36° 12-gon 1800° 150° 360° 30° quadrilateral 360° 90° 360° 90° Hide Sample Answer Question 4 The expressions in this figure represent the measures of the interior angles. Solve for the value of x .
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