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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


  • More questions

    • 1. 
      ?. x 4 ? 227 = 398
      ?. y 2 + 321 = 346

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 2. If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?

    • Options
    • A. Sunday
    • B. Saturday
    • C. Tuesday
    • D. Wednesday
    • Discuss
    • 3. 1, 4, 9, 16, 23, 25, 36

    • Options
    • A. 9
    • B. 23
    • C. 25
    • D. 36
    • Discuss
    • 4. 
      A sum of money is to be divided equally among P, Q and R in the respective ratio of 5 : 6 : 7 and another sum of money is to be divided between S and T equally. If S got ? 2100 less than P, then how much amount did Q receive?

    • Options
    • A. ? 2500
    • B. ? 2000
    • C. ? 1500
    • D. Couldn't be determined
    • Discuss
    • 5. 
      If a : b = b : c, then ratio a 4 : b 4 is equal to

    • Options
    • A. ac : b2
    • B. a2 : c2
    • C. c2 : a2
    • D. b2 : ac
    • Discuss
    • 6. 
      A man covers half of his journey at 6 km/h and the remaining half at 3 km/h. Find his average speed.

    • Options
    • A. 3 km/h
    • B. 4 km/h
    • C. 4.5 km/h
    • D. 9 km/h
    • Discuss
    • 7. 
      A person can walk a certain distance and drive back in 6 h. He can also walk both ways in 10 h. How much time will he take to drive both ways?

    • Options
    • A. 2 h
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    • C. 51/2 h
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    • Discuss
    • 8. 
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    • Options
    • A. 10
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    • 9. 
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    • Options
    • A. p2 = 2q
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    • Discuss
    • 10. 
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    • Options
    • A. 1 : 3
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