24.1 Polygons. Example 1 Ù Ù Ù Ù Ù Ù Ù Ù Ù Ù. For Free Distribution


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1 Plygns mple 1 Ù Ù Ù Ù Ù P Q T Ù Ù Ù Ù Ù R S 84 Fr Free istributin
2 24.2 Sum f the interir ngles f plygn O Ù Ù Ù Ù Ù Ù Ù Ù Ù Ù The sum f the interir ngles f plygn with n sides is (2n  4) right ngles' 85 Fr Free istributin
3 mple 1 mple 2 P 95 1 U Q T R 1 S 86 Fr Free istributin
4 = = 72 = = 125 ercise Find the sum f the interir ngles f the plygns given belw (i) Pentgn (ii) Heptgn (iii) ecgn (iv) decgn 2. Fr squre, find (i) the sum the f interir ngles (ii) the vlue f ne interir ngle 3. Fr regulr hegn, find (i) the sum f the interir ngles (ii) the vlue f ne interir ngle 4. In qudrilterl, tw interir ngles re equl. The ther tw ngles re 1 nd 8. Find the vlue f ech equl ngle. 5. Find the number f sides in regulr plygn in which ne interir ngle is Find the vlue f n interir ngle f regulr plygn with 15 sides. 7. One interir ngle f qudrilterl is 9. If the ther three ngles re equl, find the vlue f ech. 8. Find the vlue f Find the mgnitude f the remining ngles f the plygn In certin plygn, when ne verte is jined t the rest f the vertices, 5 tringles re frmed. (i) Wht is the sum f interir ngles f the plygn? (ii) Find the number f sides in the plygn. 87 Fr Free istributin
5 11. When ll the vertices f plygn re jined t pint P inside the plygn, 6 tringles re frmed. Find the (i) number f sides it hs (ii) The sum f the ngles t P (iii) The sum f the ngles f 6 tringles (iv) The sum f the interir ngles f the plygn. 12. nsider the hegn F given in the figure (i) Find the mgnitude f F nd F (ii) Shw thr F is n equilterl tringle. (iii) Find the vlue f (iv) Shw tht F is squre < < F terir ngles f plygn F When side f plygn is prduced, the ngle between the prduced prt nd the djcent side is G clled the eterir ngle. ccrdingly, Ù Ù Ù Ù G, H,, F re the eterir ngles. H y q b P s t u r t ny verte f the pentgn, the eterir nd interir ngles lie n the sme stright line. Thus + y = 18 p + q = 18 r + s = 18 u + t = 18 + b = Fr Free istributin
6 Then the sum f the interir ngles nd the eterir ngles t ll 5 vertices = 18 5 ( + y) + (p + q) + (r + s) + (u + t) + ( + b) = 18 5 ( + p + r + u + ) + (y + q + s + t + b ) = 9 ( + p + r + u + ) + 54 = 9 (s the sum f the interir ngles f pentgn is 54 ) \ ( + p + r + u + ) = 954 \ The sum f the eterir ngles f the pentgn = 36 ctivity 1 heck nd see whether the sum f the eterir ngles f qudrilterl nd hegn re ls 36 ctivity 2 mplete the tble given belw. Hence build up reltinship fr the sum f the eterir ngles f ny plygn Nme f the plygn number f sides number f vertices Sum f the eterir nd interir ngles N, f tringles frmed by verte with the ther vertices Sum f the interir ngles Sum f the eterir ngles Tringle Qudrilterl Pentgn Hegn Heptgn Octgn = = = 36 This shws tht the sum f the eterir ngles f the bve plygns is 36 The sum f eterir ngles f ny plygn is 36 mple Find the vlue f = = 36 = = Fr Free istributin
7 mple y P Find the vlues f,, y, p, in the digrm + 11 = 18 = = p = 18 p = 181 p = 8 y + 8 = 18 y = 188 y = 1 + p = = 36 (s = 7 nd p = 8 ) = 36 2 = = = = Mgnitude f n eterir ngle f regulr plygn In regulr plygn, ll the interir ngles re equl. Therefre ll the eterir ngles t re equl. ctivity 3 uild up reltinship t find the mgnitude f n eterir ngle f regulr plygn by cmpleting the tble given belw. N: f Sum f mgnitude f Nme f the N: f eterir the eterir ne eterir plygn sides ngles ngles ngle quilterl tringle = 12 Squre 4 3 Regulr pentgn Regulr hegn Regulr heptgn Regulr plygn with n sides 5 9 Fr Free istributin
8 The mgnitude f n eterir ngle f ny regulr plygn = 36 The number f sides in the plygn mple 5 Find the mgnitude f n eterir ngle f regulr plygn with 12 sides Sum f ll the eterir ngles = 36 Number f sides in the regulr plygn = 12 mgnitude f ne eterir ngle = = 3 mple 6 The eterir ngle f regulr plygn is 72. Find the number f sides in the plygn Sum f ll the eterir ngles = 36 mgnitude f ne eterir ngle = 72 \ Number f sides = = 5 ercise Find the (i) mgnitude f ne eterir ngle, (ii) mgnitude f ne interir ngle, f regulr plygn with 6 sides. 2. Find the (i) mgnitude f ne eterir ngle, (ii) mgnitude f ne interir ngle, f regulr heptgn. 3. Find the (i) mgnitude f ne eterir ngle, (ii) mgnitude f ne interir ngle, f squre. 4. Find the (i) mgnitude f ne eterir ngle, (ii) mgnitude f ne interir ngle, f n equilterl tringle. 5. Find the (i) mgnitude f ne eterir ngle, (ii) mgnitude f ne interir ngle, f regulr plygn with 8 sides. 6. The eterir ngle f regulr plygn is 6. Find (i) the number f sides. 91 Fr Free istributin
9 (ii) the mgnitude f ne interir ngle, 7. Fr regulr plygn in which ne eterir ngle is 36, find (i) the number f sides. (ii) the mgnitude f ne interir ngle. 8. Fr regulr plygn in which ne eterir ngle is 45, find (i) the number f sides. (ii) mgnitude f ne interir ngle. 9. Fr regulr plygn in which ne eterir ngle is 2, find (i) the number f sides. (ii) the mgnitude f ne interir ngle. 1. Fr regulr plygn in which ne interir ngle is14, find (i) the mgnitude f ne eterir ngle. (ii) the number f sides. 11. In regulr plygn, n interir ngle is equl t twice the eterir ngle, find (i) the mgnitude f n eterir ngle (ii) the mgnitude f n interir ngle e f (iii) the number f sides (iv) the sum f the interir ngles. 12. ccrding t the infrmtin given in the digrm, find the mgnitude f the ngles, b, c, d, e, f ccrding t the infrmtin given in the digrm, (i) find the mgnitude f (ii) find the mgnitude f the ngles, b, c, 7 12 b 14. The mgnitude f ne eterir ngle f regulr plygn is 4. Find (i) the number f sides in the plygn (ii) the mgnitude f n interir ngle (iii) the sum f the interir ngles f the plygn. c b 3 c 5 n there be regulr plygn with ne eterir ngle equl t 64? Give resns fr yur nswer. 92 Fr Free istributin
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