{"id":3647,"date":"2024-01-30T12:28:15","date_gmt":"2024-01-30T06:28:15","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=3647"},"modified":"2024-10-29T15:36:20","modified_gmt":"2024-10-29T09:36:20","slug":"angle-between-non-parallel-lines","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/angle-between-non-parallel-lines\/","title":{"rendered":"\u09a6\u09c1\u0987\u099f\u09bf \u0985\u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09b0\u09c7\u0996\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u0995\u09cb\u09a3, \u09a6\u09c1\u0987\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac, \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u098f\u09ac\u0982 \u09b2\u09ae\u09cd\u09ac \u09b9\u0993\u09df\u09be\u09b0 \u09b6\u09b0\u09cd\u09a4"},"content":{"rendered":"

\u09a6\u09c1\u0987\u099f\u09bf \u0985\u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09b0\u09c7\u0996\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u0995\u09cb\u09a3 (<\/b>Angle <\/b>between two non-parallel straight lines)<\/b><\/h2>\n

\u09a6\u09c1\u0987\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be\u09b0 \u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u09ad\u09c1\u0995\u09cd\u09a4 \u0995\u09cb\u09a3 \u09a8\u09bf\u09b0\u09cd\u09a3\u09df \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964\u00a0<\/b><\/p>\n

    \n
  1. \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, AB \u0993 AC \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09a6\u09c1\u0987\u099f\u09bf\u09b0 \u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u09ad\u09c1\u0995\u09cd\u09a4 \u0995\u09cb\u09a3 <\/span> \\theta <\/span> ;<\/span><\/li>\n<\/ol>\n

    \u09a4\u09be\u09b9\u09b2\u09c7, <\/span>\u00a0 \\angle B A C=\\theta <\/span><\/p>\n

    \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <\/span> \\angle A B X=\\theta_1 <\/span><\/span>\u00a0\u098f\u09ac\u0982 <\/span> \\angle A C X=\\theta_2 <\/span><\/span> \u098f\u09ac\u0982 \\theta_1 > \\theta_2 <\/span><\/span>\u00a0<\/span>\u00a0\u00a0\u00a0<\/span><\/p>\n \\therefore \\theta=\\theta_{1}-\\theta_{2} \\quad \\cdots \\quad \\ldots \\quad \\ldots \\text { (i) } <\/span>\n

    AB \u0993 AC \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09a6\u09c1\u0987\u099f\u09bf\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u00a0<\/span><\/p>\n

    \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf,\u00a0 y=m_{1} x+c_{1} \\text { \u098f\u09ac\u0982 } y=m_{2} x+c_{2} <\/span><\/span><\/p>\n

    \u09a4\u09be\u09b9\u09b2\u09c7 \\tan \\theta_{1}=m_{1} \\text { \u098f\u09ac\u0982 } \\tan \\theta_{2}=m_{2} <\/span><\/span>\u00a0\u00a0<\/span><\/p>\n

    (i) \u09a8\u0982 \u09a5\u09c7\u0995\u09c7 \u09aa\u09be\u0987,\u00a0 \\tan \\theta=\\tan \\left(\\theta_{1}-\\theta_{2}\\right) <\/span><\/span><\/p>\n =\\frac{\\tan \\theta_{1}-\\tan \\theta_{2}}{1+\\tan \\theta_{1} \\tan \\theta_{2}} <\/span>\n

    \u0985\u09b0\u09cd\u09a5\u09be\u09ce, \\tan \\theta=\\frac{m_{1}-m_{2}}{1+m_{1} m_{2}} <\/span><\/span>.<\/span> \u098f\u0987 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09b9\u09a4\u09c7 <\/span> \u098f\u09b0 \u09ae\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a3\u09df \u0995\u09b0\u09be \u09af\u09be\u09df\u0964\u00a0<\/span><\/p>\n

    \u09a8\u09cb\u099f\u0983<\/b> \\theta_{2}>\\theta_{1} \\text { \u09b9\u09b2\u09c7, } \\theta=\\theta_{2}-\\theta_{1}=-\\left(\\theta_{1}-\\theta_{2}\\right) <\/span><\/p>\n \\therefore \\tan \\theta=\\tan \\left\\{-\\left(\\theta_{1}-\\theta_{2}\\right)\\right\\}=-\\tan \\left(\\theta_{1}-\\theta_{2}\\right) <\/span>\n =-\\frac{\\tan \\theta_{1}-\\tan \\theta_{2}}{1+\\tan \\theta_{1} \\tan \\theta_{2}} <\/span>\n =-\\frac{m_{1}-m_{2}}{1+m_{1} m_{2}} <\/span>\n

    \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987,\u00a0 \u00a0 \\tan \\theta=\\pm \\frac{m_{1}-m_{2}}{1+m_{1} m_{2}} <\/span><\/span><\/p>\n

    \\tan \\theta <\/span> <\/span>\u098f\u09b0 \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u0993 \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u09ae\u09be\u09a8 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 \u09b0\u09c7\u0996\u09be \u09a6\u09c1\u0987\u099f\u09bf\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09b8\u09c2\u0995\u09cd\u09b7\u09cd\u09ae\u0995\u09cb\u09a3 \u0993 \u09b8\u09cd\u09a5\u09c2\u09b2\u0995\u09cb\u09a3\u09c7\u09b0 \u09ae\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6 \u0995\u09b0\u09c7\u0964\u00a0\u00a0<\/span><\/p>\n

      \n
    1. \u09af\u09a6\u09bf \u09a6\u09c1\u0987\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 a_{1} x+b_{1} y+c_{1}=0 <\/span><\/span>\u00a0<\/span>\u098f\u09ac\u0982 a_{2} x+b_{2} y+c_{2}=0 <\/span><\/span>\u00a0<\/span>\u09b9\u09df, \u09a4\u09ac\u09c7 \u09a4\u09be \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09a6\u09cd\u09ac\u09df\u0995\u09c7 \u09a2\u09be\u09b2\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u0986\u0995\u09be\u09b0\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09c7 \u09aa\u09be\u0987,\u00a0<\/span><\/li>\n<\/ol>\n y=-\\frac{a_{1}}{b_{1}} \\times-\\frac{c_{1}}{b_{1}} <\/span>\n

      \u098f\u09ac\u0982, y=-\\frac{a_{2}}{b_{2}} \\times-\\frac{c_{2}}{b_{2}} <\/span><\/span><\/p>\n

      \u098f\u0996\u09be\u09a8\u09c7 \u09b0\u09c7\u0996\u09be \u09a6\u09c1\u0987\u099f\u09bf\u09b0 \u09a2\u09be\u09b2 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7,\u00a0<\/span><\/p>\n m_{1}=-\\frac{a_{1}}{b_{1}} \\text { \u098f\u09ac\u0966, } m_{2}=-\\frac{a_{2}}{b_{2}} <\/span>\n \\therefore \\tan \\theta=\\pm \\frac{-\\frac{a_{1}}{b_{2}}+\\frac{a_{2}}{b_{2}}}{1+\\frac{a_{1} a_{2}}{b_{1} b_{2}}} <\/span>\n =\\pm \\frac{a_{2} b_{1}-a_{1} b_{2}}{a_{1} a_{2}+b_{1} b_{2}} <\/span>\n

      \"Angle\"<\/p>\n

      \u09a6\u09c1\u0987\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac \u09b9\u0993\u09df\u09be\u09b0 \u09b6\u09b0\u09cd\u09a4 <\/b>(Condition of perpendicular of two straight lines)\u00a0<\/b><\/h2>\n

      \u09a6\u09c1\u0987\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac \u09b9\u0993\u09df\u09be\u09b0 \u09b6\u09b0\u09cd\u09a4 \u09b9\u099a\u09cd\u099b\u09c7, \u098f\u09a6\u09c7\u09b0 \u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u09ad\u09c1\u0995\u09cd\u09a4 \u0995\u09cb\u09a3 \u09b8\u09ae\u0995\u09cb\u09a3 \u09b9\u0993\u09df\u09be \u0985\u09b0\u09cd\u09a5\u09be\u09ce \\theta_{2}=\\theta_{1}+90^{\\circ} <\/span><\/span>\u0985\u09a5\u09ac\u09be \u00a0\\theta_{1} = \\theta_{2} + 90^{\\circ}<\/span><\/span>\u00a0 \u09af\u0996\u09a8 (\u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7) \\theta_{2}>\\theta_{1} \\text { \u09ac\u09be } \\theta_{1}>\\theta_{2} <\/span><\/span><\/p>\n

      \u098f\u0996\u09a8, m_{2}=\\tan \\theta_{2}=\\tan \\left(\\theta_{1}+90^{\\circ}\\right)=-\\cot \\theta_{1}=-\\frac{1}{m_{1}} <\/span><\/span><\/p>\n

      \u0985\u09a5\u09ac\u09be, m_{1}=\\tan \\theta_{1}=\\tan \\left(\\theta_{2}+90^{\\circ}\\right)=-\\cot \\theta_{2}=-\\frac{1}{m_{2}} <\/span><\/span>\u00a0\u09b9\u09ac\u09c7\u0964\u00a0<\/span><\/p>\n m_{1} m_{2}=-1 \\quad \\ldots \\quad \\ldots <\/span>\n

      \u0985\u09a8\u09c1\u09b0\u09c2\u09aa\u09ad\u09be\u09ac\u09c7, a_{1} x+b_{1} y+c_{1}=0 <\/span><\/span><\/p>\n

      \u098f\u09ac\u0982 a_{2} x+b_{2} y+c_{2}=0 <\/span><\/span>\u00a0\u09b0\u09c7\u0996\u09be \u09a6\u09c1\u0987\u099f\u09bf\u09b0 \u09b2\u09ae\u09cd\u09ac \u09b9\u0993\u09df\u09be\u09b0 \u09b6\u09b0\u09cd\u09a4 \u09b9\u09b2\u09cb\u00a0<\/span><\/p>\n \\left(-\\frac{a_{1}}{b_{1}}\\right)=\\left(-\\frac{a_{2}}{b_{2}}\\right)=-1 <\/span>\n

      \u09ac\u09be,\u00a0 a_{1} a_{2}+b_{1} b_{2}=0 <\/span><\/span><\/p>\n

      \u0985\u09a4\u098f\u09ac, \u09a6\u09c7\u0996\u09be \u09af\u09be\u099a\u09cd\u099b\u09c7 \u09af\u09c7, \u09a6\u09c1\u0987\u099f\u09bf \u09b0\u09c7\u0996\u09be \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac \u09b9\u0993\u09df\u09be\u09b0 \u09b6\u09b0\u09cd\u09a4 \u09b9\u099a\u09cd\u099b\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0 \u09a2\u09be\u09b2\u09a6\u09cd\u09ac\u09df\u09c7\u09b0 \u0997\u09c1\u09a3\u09ab\u09b2 -1 \u09b9\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964 \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac\u09b0\u09c7\u0996\u09be\u09a6\u09cd\u09ac\u09df\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a8\u09bf\u09ae\u09cd\u09a8\u09b2\u09bf\u0996\u09bf\u09a4\u09ad\u09be\u09ac\u09c7 \u09b2\u09c7\u0996\u09be \u09af\u09be\u09df\u0964\u00a0<\/span><\/p>\n

        \n
      1. \u00a0 \u00a0 \\mathrm{y}=m_{1} \\mathrm{x}+c_{1} \\text { \u098f\u09ac\u0982 } \\mathrm{y}=-\\frac{1}{m} x+c_{2} <\/span><\/span><\/li>\n<\/ol>\n

        \u0995\u09be\u09b0\u09a3, m_{1} m_{2}=\\left(-\\frac{1}{m_{1}}\\right)=-1 <\/span><\/span><\/p>\n

        \u098f\u0995\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be\u09b0 \u09a2\u09be\u09b2 m \u09b9\u09b2\u09c7,\u00a0<\/span><\/p>\n

        \u09a4\u09be\u09b0 \u0989\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac\u09b0\u09c7\u0996\u09be\u09b0 \u09a2\u09be\u09b2 - \\frac{1}{m}= <\/span><\/span>\u00a0\u09b9\u09ac\u09c7,\u00a0<\/span><\/p>\n

          \n
        1. \u00a0 \u00a0 \\mathrm{ax}+\\mathrm{by}+c_{1}=0 <\/span><\/span><\/li>\n<\/ol>\n

          \u098f\u09ac\u0982 \\mathrm{bx}+\\mathrm{ay}+c_{2}=0 <\/span><\/span><\/p>\n

          \u0995\u09be\u09b0\u09a3 a_{1} a_{2}+b_{1} b_{2}=a b+b(-a)=a b-a b=0 <\/span><\/span><\/p>\n

          iii.\u00a0 \u00a0 3 x-2 y=5 \\text { \u098f\u09ac\u0982 } 2 x+3 y=7 <\/span><\/span><\/p>\n

          \u0995\u09be\u09b0\u09a3 a_{1} a_{2}+b_{1} b_{2}=3 \\times 2+(-2) \\times 3 <\/span><\/span><\/p>\n

          = 6 \u2013 6 = 0<\/span><\/p>\n

          \u0985\u09a4\u098f\u09ac, \u09a6\u09c7\u0996\u09be \u09af\u09be\u099a\u09cd\u099b\u09c7 \u09af\u09c7, \u098f\u0995\u099f\u09bf \u09b0\u09c7\u0996\u09be\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 \u0993 \u098f\u09b0 \u09b8\u09b9\u0997 \u09a6\u09c1\u0987\u099f\u09bf \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8 \u0995\u09b0\u09be\u09b0 \u09aa\u09b0, \u098f\u09a6\u09c7\u09b0 \u09af\u09c7 \u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf\u09b0 \u099a\u09bf\u09b9\u09cd\u09a8 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8 \u0995\u09b0\u09c7, \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 \u09aa\u09a6\u099f\u09bf\u0995\u09c7 \u0987\u099a\u09cd\u099b\u09c7\u09ae\u09a4\u09cb \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8 \u0995\u09b0\u09c7 \u09a8\u09bf\u09b2\u09c7 \u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09c7\u0996\u09be\u09b0 \u0989\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac \u0985\u09aa\u09b0 \u098f\u0995\u099f\u09bf \u09b0\u09c7\u0996\u09be\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09df\u0964\u00a0<\/span><\/p>\n

          \u09a6\u09c1\u0987\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u098f\u09ac\u0982 \u09b2\u09ae\u09cd\u09ac \u09b9\u0993\u09df\u09be\u09b0 \u09b6\u09b0\u09cd\u09a4 <\/b>(Condition of parallel and perpendicular of two straight lines)<\/b><\/h2>\n

          \u09a6\u09c1\u0987\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09b9\u09ac\u09c7, \u09af\u09a6\u09bf \u0993 \u0995\u09c7\u09ac\u09b2 \u09af\u09a6\u09bf \u09a4\u09be\u09b0\u09be x \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u09a6\u09bf\u0995\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u09b8\u09ae\u09be\u09a8 \u0995\u09cb\u09a3 \u0989\u09ce\u09aa\u09a8\u09cd\u09a8 \u0995\u09b0\u09c7\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09b0\u09c7\u0996\u09be\u09a6\u09cd\u09ac\u09df\u09c7\u09b0 \u09a2\u09be\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8 \u09b8\u09ae\u09be\u09a8 \u09b9\u09df\u0964\u00a0\u00a0<\/span><\/p>\n

          \u09b8\u09c1\u09a4\u09b0\u09be\u0982, y = m_{1} x + c_{1} <\/span><\/span><\/p>\n

          \u098f\u09ac\u0982\u00a0 y = m_{2} x + c_{2} <\/span><\/span>\u00a0<\/span>\u09b0\u09c7\u0996\u09be \u09a6\u09c1\u0987\u099f\u09bf\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09b9\u0993\u09df\u09be\u09b0 \u09b6\u09b0\u09cd\u09a4 \\theta_1 = \\theta_2 <\/span><\/span><\/p>\n

          \u09b8\u09c1\u09a4\u09b0\u09be\u0982, \\tan \\theta_1 = \\tan \\theta_2 <\/span><\/span><\/p>\n

          \u09ac\u09be,\u00a0 m_{1} = m_{2} <\/span><\/span><\/p>\n

          \u0985\u09a8\u09c1\u09b0\u09c2\u09aa\u09ad\u09be\u09ac\u09c7, a_{1} x+b_{1} y+c_{1}=0\u00a0 <\/span><\/span><\/p>\n

          \u098f\u09ac\u0982 <\/span> a_{2} x+b_{2} y+c_{2}=0\u00a0 <\/span><\/span> \u09b0\u09c7\u0996\u09be \u09a6\u09c1\u0987\u099f\u09bf\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09b9\u0993\u09df\u09be\u09b0 \u09b6\u09b0\u09cd\u09a4 -\\frac{a_{1}}{b_{1}}=-\\frac{a_{2}}{b_{2}} <\/span><\/span><\/p>\n

          \u09ac\u09be,\u00a0 \\frac{a_{1}}{b_{1}}= \\frac{a_{2}}{b_{2}} <\/span><\/span><\/p>\n

          \u0989\u09aa\u09b0\u09c7\u09b0 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u0997\u09c1\u09b2\u09bf \u09a5\u09c7\u0995\u09c7 \u098f\u099f\u09be \u09aa\u09b0\u09bf\u09b7\u09cd\u0995\u09be\u09b0 \u09af\u09c7, \u09a6\u09c1\u0987\u099f\u09bf\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09b0\u09c7\u0996\u09be\u0995\u09c7 \u09a8\u09bf\u09ae\u09cd\u09a8\u09b2\u09bf\u0996\u09bf\u09a4\u09ad\u09be\u09ac\u09c7 \u09b2\u09c7\u0996\u09be \u099a\u09b2\u09c7, \u09af\u09c7\u09b9\u09c7\u09a4\u09c1 \u09a4\u09be\u09a6\u09c7\u09b0 \u09a2\u09be\u09b2 \u09b8\u09ae\u09be\u09a8\u0964<\/span><\/p>\n

            \n
          1. \\mathrm{y}=\\mathrm{m} \\mathrm{x}+\\mathrm{c}_{1} \\quad \\text { \u098f\u09ac\u0982 } \\mathrm{y}=\\mathrm{mx}+\\mathrm{c}_{2} <\/span><\/li>\n
          2. \\mathrm{ax}+\\mathrm{by}+c_{1}=0 \\quad \\text { \u098f\u09ac\u0982 } \\mathrm{ax}+\\mathrm{by}+c_{2}=0 <\/span><\/li>\n<\/ol>\n

            3.\u00a0 4 x-3 y=7 \\quad \\text { \u098f\u09ac\u0982 } 4 x-3 y=12 <\/span><\/span><\/p>\n

            \u0985\u09a4\u098f\u09ac, \u09a6\u09c7\u0996\u09be \u09af\u09be\u099a\u09cd\u099b\u09c7 \u09af\u09c7, \u09a6\u09c1\u0987\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 \u09af\u09a6\u09bf \u0995\u09c7\u09ac\u09b2 \u09a4\u09be\u09a6\u09c7\u09b0 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 \u09aa\u09a6\u099f\u09bf \u09ad\u09bf\u09a8\u09cd\u09a8 \u09b9\u09df \u09a4\u09ac\u09c7 \u09a4\u09be\u09b0\u09be \u098f\u0995 \u099c\u09cb\u09dc\u09be \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u099c\u09cd\u099e\u09be\u09aa\u09a8 \u0995\u09b0\u09c7\u0964 \u0985\u09a4\u098f\u09ac, \u098f\u0995\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 x \u0993 y \u098f\u09b0 \u09b8\u09b9\u0997 \u09b8\u09cd\u09a5\u09bf\u09b0 \u09b0\u09c7\u0996\u09c7 \u09a4\u09be\u09b0 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 \u09aa\u09a6\u099f\u09bf \u0987\u099a\u09cd\u099b\u09c7\u09ae\u09a4\u09cb \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8 \u0995\u09b0\u09b2\u09c7 \u098f\u0995\u099f\u09bf \u09b0\u09c7\u0996\u09be\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09df\u0964\u00a0<\/span><\/p>\n

            \"Angle\"<\/p>\n","protected":false},"excerpt":{"rendered":"

            \u09a6\u09c1\u0987\u099f\u09bf \u0985\u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09b0\u09c7\u0996\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u0995\u09cb\u09a3 (Angle between two non-parallel straight lines) \u09a6\u09c1\u0987\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be\u09b0 \u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u09ad\u09c1\u0995\u09cd\u09a4 \u0995\u09cb\u09a3 \u09a8\u09bf\u09b0\u09cd\u09a3\u09df \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964\u00a0 \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, AB \u0993 AC \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09a6\u09c1\u0987\u099f\u09bf\u09b0 \u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u09ad\u09c1\u0995\u09cd\u09a4 \u0995\u09cb\u09a3 ; \u09a4\u09be\u09b9\u09b2\u09c7, \u00a0 \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, \u00a0\u098f\u09ac\u0982 \u098f\u09ac\u0982 \u00a0\u00a0\u00a0\u00a0 AB \u0993 AC \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09a6\u09c1\u0987\u099f\u09bf\u09b0<\/p>\n

            Read More<\/a><\/p>\n","protected":false},"author":56,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[4258,3037,3026],"tags":[2526,2525,2524,2523],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3647"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/56"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=3647"}],"version-history":[{"count":14,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3647\/revisions"}],"predecessor-version":[{"id":16096,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3647\/revisions\/16096"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=3647"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=3647"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=3647"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}