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7, Mathematics, Quarter 3 – Module 8:, Solving Problems Involving Side, and Angle of a Polygon, , CO_Q3_Mathematics 7_ Module 8

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Mathematics – Grade 7, Alternative Delivery Mode, Quarter 3 – Module 8: Solving Problems Involving Side and Angle of a Polygons, First Edition, 2020, Republic Act 8293, section 176 states that: No copyright shall subsist in any work, of the Government of the Philippines. However, prior approval of the government agency or, office wherein the work is created shall be necessary for exploitation of such work for profit., Such agency or office may, among other things, impose as a condition the payment of, royalties., Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names,, trademarks, etc.) included in this module are owned by their respective copyright holders., Every effort has been exerted to locate and seek permission to use these materials from, their respective copyright owners. The publisher and authors do not represent nor claim, ownership over them., Published by the Department of Education, Secretary: Leonor Magtolis Briones, Undersecretary: Diosdado M. San Antonio, Development Team of the Module, Writer:, , Arnel C. Lapitan, , Editor:, , Venus Jane E. Rosete, , Reviewer:, , Reynaldo C. Tagala, , Layout Artist:, , Maylene F. Grigana, , James B. De Los Reyes, , Management Team: Allan G. Farnazo, CESO IV, Regional Director, Gilbert B. Barrera, Chief, CLMD, Arturo D. Tingson Jr., REPS, LRMS, Peter Van C. Ang-ug, REPS, ADM, Donna S. Panes, CID Chief, Elizabeth G. Torres, EPS - LRMS, Judith B. Alba, Division ADM Coordinator, , Printed in the Philippines by_______________________, Department of Education – SOCCSKSARGEN - Region XII, Office Address:, Telefax:, E-mail Address:, , Regional Center, Brgy. Carpenter Hill, City of Koronadal, (083) 2288825/ (083)2281893, [email protected]

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7, Mathematics, Quarter 3 – Module 8:, Solving Problems Involving Side, and Angle of a Polygons

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Introductory Message, This Self-Learning Module (SLM) is prepared so that you, our dear learners,, can continue your studies and learn while at home. Activities, questions, directions,, exercises, and discussions are carefully stated for you to understand each lesson., Each SLM is composed of different parts. Each part shall guide you step-bystep as you discover and understand the lesson prepared for you., Pre-tests are provided to measure your prior knowledge on lessons in each, SLM. This will tell you if you need to proceed on completing this module or if you, need to ask your facilitator or your teacher’s assistance for better understanding of, the lesson. At the end of each module, you need to answer the post-test to self-check, your learning. Answer keys are provided for each activity and test. We trust that you, will be honest in using these., In addition to the material in the main text, Notes to the Teacher are also, provided to our facilitators and parents for strategies and reminders on how they, can best help you on your home-based learning., Please use this module with care. Do not put unnecessary marks on any part, of this SLM. Use a separate sheet of paper in answering the exercises and tests. And, read the instructions carefully before performing each task., If you have any questions in using this SLM or any difficulty in answering the, tasks in this module, do not hesitate to consult your teacher or facilitator., Thank you.

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What I Need to Know, This module was designed and written with you in mind. It is here to help, you learn solving problems involving side and angle of polygons. The scope of this, module may be used in many different learning situations. The language used, recognizes your vocabulary level. The lessons are arranged to follow the standard, sequence of the course. But the order in which you study can be rearranged to, correspond with the textbook you are now using., , The lesson presented in this module is:, 1. Sides and angles of a polygons, After going through this module, you are expected to:, 1. Solve problems involving sides and angle of a polygons., , 1, , CO_Q3_Mathematics 7_ Module 8

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What I Know, Multiple choice. Read each item carefully. Choose the letter of the best answer, and write it on a separate sheet of paper., 1. What is the sum of the measures of the vertex angles of octagon?, A. 1,0800, B. 9000, C. 1,2600, D. 7200, 2. What is the sum of the measures of the vertex angles of a pentagon?, A. 5400, B. 3600, C. 7200, D. 9000, 3. The number of sides of the polygons with 1,2600 as the sum of the measures, of the vertex angles is _____., A. 6, B. 7, C. 8, D. 9, 4. What is the number of sides of the polygons when the sum of the measures of, the vertex angles is 1,6200?, A. 11, B. 12, C. 13, D. 14, 5., , What is the perimeter of an isosceles triangle with the base measuring 12.3, cm. and one of the equal sides equal to 15cm?, A. 27.3 cm, B. 27.3 cm2, C. 42.3 cm, D. 42.3 cm2, , 6. What is the sum of all interior angle of a polygon having 29 sides?, A. 4,8600, B. 5,0400, C. 5,2200, D. 5,4000, , 2, , CO_Q3_Mathematics 7_ Module 8

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7. If the sum of the measure of the interior angle of a polygon is 3,240, what is, the number of sides of the polygon?, A. 18, B. 19, C. 20, D. 21, 8. What is the sum of the interior angles of a decagon?, A. 900, B. 1800, C. 3600, D. 1,4400, 9. The sum of all interior angles of a polygon is 3,0600. How many sides does the, polygon have?, A. 12, B. 14, C. 17, D. 19, 10. What is the measure of each interior angle of a regular polygon with 9 sides?, , A., B., C., D., , 900, 1400, 1600, 2400, , 3, , CO_Q3_Mathematics 7_ Module 8

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Lesson, , 1, , Solving Problems Involving, Side and Angle of a Polygon, , In this lesson, you will learn how to solve problems involving side and angle, of a polygon., , What’s In, Recall that a polygon is a closed figure made up of three or more line, segments joined at their endpoints. When all sides and all angles of a polygons, are congruent, the polygons is a regular polygons or regular n-gon., , Illustrative examples:, Find the perimeter of each polygon., , A. Pentagon with a sides 5cm, B. Equilateral triangle with sides 7cm, C. Square with sides 26mm, Solution:, , A., , Pentagon with sides 5cm, P = s1 + s2 + s3 + s4 + s5, = 5 cm + 5 cm + 5 cm + 5 cm + 5 cm, = 25 cm, , B., , Equilateral triangle with sides 7cm, P = s1 + s2 + s3, = 7 cm + 7 cm + 7 cm, = 21 cm, , C., , Square with sides 26mm, P = s1 + s2 + s3 + s4, = 26 mm + 26 mm + 26 mm + 26 mm, = 104 mm, , 4, , CO_Q3_Mathematics 7_ Module 8

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What’s New, To help you understand problems involving sides and angles of a polygon,, recall that the sum of the measures of the interior angles of a triangle is 180 0. Now,, try to determine inductively the sum of the measures of the interior angles of any, polygon by doing the following activity., Activity 1., , 1. Draw convex polygons with four, five, six, seven and eight sides., 2. Divide each polygon into triangles by drawing diagonals from one of its, vertices., 3. Find the sum of the measures of the interior angles of each polygon by, multiplying the number of triangles formed by 1800., 4. Record all the resulting values in a separate sheet of paper using a, table similar to table 1.1. The first one has been done for you., Table 1.1 Sum of the Interior Angles of a Polygon, Polygon, , No. of, Sides, , Quadrilateral, , 4, , No. of Triangles Formed, in the Figure, F, E, , Sum of the Angle, Measure, , 2 x 1800 = 3600, A, , R, 2, , Pentagon, , 5, ______ x 1800 = _____, _____, , Hexagon, , 6, , ____ x 1800 = _____, , _____, , Heptagon, , 7, , ______ x 1800 = _____, _____, , 5, , CO_Q3_Mathematics 7_ Module 8

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Octagon, , 8, , ______ x 1800 = _____, , _____, , Remember!, The sum of the measures of the interior angles of an n-gon is ,, , 11., , S = (n – 2 )1800, where n is the number of sides., , Questions:, What did you discover? What is the sum of the measures of the interior, angles of a polygon with 10 sides? of an n-gon?, , What is It, , The sum of the measures of the interior angles of an n-gon is, S = (n – 2, where n is the number of sides. The sum of the measures of the exterior, angles of any polygon is equal to 360 0. The measure of each angle of a regular, )1800,, , polygon with n sides is, , (𝒏−𝟐)𝟏𝟖𝟎𝟎, 𝒏, , ., , Example 1. Find the sum of the measures of the vertex angles for pentadecagon., Solution: Pentadecagon is a 15-sided polygon, S = ( n – 2)1800, = ( 15 – 2 ) 1800, = ( 13 ) 1800, = 2,3400, Therefore, the sum of the measures of the angles of a pentadecagon is 2,3400., , 6, , CO_Q3_Mathematics 7_ Module 8

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Example 2. Find the number of sides of a regular polygon when the measure, of an exterior angle is 450., , Solution:, Recall that each exterior angle of a regular polygon measures 3600/n. Since, each exterior angle measures 450, hence,, 450 = 3600/n, 450n = 3600, n = 3600/450, n=8, , Therefore, the polygon has 8 sides., , What’s More, Activity 1. Draw the figure as a guide. Eddie estimated that he would need at, least 1 meter of wooden sidings to make a picture frame. What are the dimensions, of the largest frame he could make if the frame is, , a. a square?, b. rectangular shape?, c. pentagon?, , Activity 2, For their project in TLE, Belen decided to sew red piping along the edges of, the table cloth measures 1.75m by 2.85m, at least how many meters of piping, should she prepare?, , 7, , CO_Q3_Mathematics 7_ Module 8

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What I Have Learned, , On a separate sheet of paper, match the correct answer in column B. Write only, the letter of your answer in the space provided., Column A, Column B, 1., 2., 3., 4., , 5., , Find the sum of the measures of the, vertex angles for octagon., Find the sum of the measures of the, vertex angles for hexagon, Find the sum of the measures of the, vertex angles for heptagon, Find the number of sides of the, regular polygon when the sum of the, measures of the vertex angle is 1,2600, Find the number of sides of the, regular polygon when the sumof the, measures of the vertex angle is 1,9800, , a., b., c., d., e., f., , 9000, 9, 1,0800, 13, 7200, 1,2600, , Good job! Now you’re up for the next challenge of this lesson., , What I Can Do, , Activity 3, Use your learning on solving problems involving sides and angles of, polygons., A six sided regular polygon is inscribed in a circle of radius 10cm, find, the length of one side of hexagon., Excellent work! You did a good job in applying what you have learned!, , 8, , CO_Q3_Mathematics 7_ Module 8

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Assessment, Multiple choice. Read each item carefully. Choose the letter of the best answer, and write it on a separate sheet of paper., 1. Find the sum of the interior angles of a heptagon., A. 9000, B. 1350, C. 1,8000, D. 400, 2. Find the interior angle of a regular octagon., A. 1600, B. 1350, C. 1,8000, D. 400, 3. Find the measure of each interior angle, each exterior angle and the sum of, the interior angle of a regular dodecagon., A. 1500 , 400, 18000, B. 1500 , 600, 18000, C. 1500 , 300, 18000, D. 1500 , 200, 18000, 4., , Jacob has a large sandbox, the sandbox is 12meters long and 8meters wide., He wants to surround the sandbox with new pieces of wood. How many, meters of wood will he need?, A. 40 meters, B. 50 meters, C. 60 meters, D. 70 meters, , 5., , The perimeter of Sophia’s Garden is 42 meters. The garden is 6 meters wide., What is the length of the garden?, A. 30 meters, B. 25 meters, C. 15 meters, D. 10 meters, , 9, , CO_Q3_Mathematics 7_ Module 8

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6. What is the sum of all interior angle of a regular hexagon?, A. 5400, B. 7200, C. 1,2600, D. 1,4400, 7. If the sum of the measure of the interior angle of a polygon is 2,1600, what is, the number of sides of the polygon?, A. 11, B. 12, C. 13, D. 14, 8. What is the measure of each interior angle of a regular octagon?, A. 1350, B. 1800, C. 3600, D. 5400, 9. A regular polygon has an exterior angle that measures 40 0. How many sides, does the polygon have?, A. 7, B. 8, C. 9, D. 10, 10. What is the measure of each interior angle of a polygon with 12 sides?, A. 1200, B. 1400, C. 1500, D. 1600, , Additional Activities, In each of the following polygons, find the sum of the interior angles and the, sum of exterior angles., , 1. Hexagon, 2. Octagon, , 10, , CO_Q3_Mathematics 7_ Module 8

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11, , CO_Q3_Mathematics 7_ Module 8, , What’s New, , What I Know, 1. A, 2. A, 3. D, 4. A, 5. C, 6. A, 7. C, 8. D, 9. D, 10.B, , No. of, triangles, formed in the, figure, , Sum of the, angle measure, , What Can I Do, 1. 10cm, , 2, 3, 4, 5, 6, , 3600, 5400, 7200, 9000, 10800, , What's More, Activity 1, , What I have learned, 1. c, 2. e, 3. a, 4. b, 5. d, , 1. S = 25cm, 2. W =254cm,, L =25cm, 3. S = 20cm, , Activity 2, , 1. 9.2 meter, , Assessment, 1. A, 2. B, 3. C, 4. A, 5. C, 6. B, 7. D, 8. A, 9. C, 10.C, , Additional Activity, 1. Sum of interior, angle is 7200, Sum of exterior, angle is 3600, 2. Sum of interior, angle is 10800, Sum of exterior, angle is 3600, , Answer Key

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References, Department of Education-National Program Support for Basic Education, Elementary Algebra for First Year., Department of Education-Instructional Materials Council Secretariat, ( DepEd – IMCS), Mathematics – Grade 7 Teachers Guide First Edition, 2013, ISBN: 978-971-9990-61-1, Charles P Mckeague, et.al. (2013). Basic College Mathematics Anvil, Publishing,, Inc., Mandaluyong, City, 1550, Philippines, , 12, , CO_Q3_Mathematics 7_ Module 8