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Home Aptitude Plane Geometry See What Others Are Saying!
  • Question
  • In the given figure, ?B = ?C = 55° and ?D = 25°. Then:


  • Options
  • A. BC < CA < CD
  • B. BC > CA > CD
  • C. BC < CA, CA > CD
  • D. BC > CA, CA < CD

  • Correct Answer
  • BC > CA, CA < CD 

    Explanation

    According to question,
    ?B = ?C = 55° , ?D = 25°
    We can say ,
    AB = AC ( ? ?B = ?C = 55° )
    In Triangle ABC,
    ?A + ?B + ?C = 180°
    ? ?A + 55° + 55° = 180°
    ? ?A + 110° = 180°
    ? ?A = 180° - 110°
    ? ?A = 70° ..........................(1)
    As per given figure,
    ?ACD + ?ACB = 180° ( ?ACB = ?C = 55°)
    ? ?ACD + 55° = 180°
    ? ?ACD = 180° - 55°
    ? ?ACD = 125° ....................... (2)
    Now in Triangle ACD,
    ?CAD + ?ACD + ?CDA = 180°
    ? ?CAD + 125° + 25° = 180°
    ? ?CAD + 150° = 180°
    ? ?CAD = 30° ...........................(3)
    ( In a ?, greater angle has longer side opposite to it )
    From the equation (1) , (2) and (3);
    ?B < ?A and ?CAD > ?D ;
    ? BC > CA and CA < CD


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