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Another Point In A Square (Posted on 2004-06-11) Difficulty: 3 of 5
There is a point M inside a square ABCD such that angle MAB is 60 and angle MCD is 15. Find angle MBC.

See The Solution Submitted by Brian Smith    
Rating: 3.2500 (4 votes)

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re: Solution - another method | Comment 10 of 16 |
(In reply to Solution - another method by Telly)

The three equations you "solve" (x + z = 120, y - z = 15, y + x = 135)  are not independent.  You derived one from the other two.  There are many solutions.

Of the requirements that you list, only that z<90 is apparent from the diagram.  But in fact all your requirements are met by quite a range of solutions.

  x       y       z
 119      16       1
 110      25      10
 100      35      20
  90      45      30
  88      47      32
  86      49      34
  84      51      36
  82      53      38
  80      55      40
  78      57      42
  76      59      44
  74      61      46
  72      63      48
  70      65      50
  68      67      52
  66      69      54
  64      71      56
  62      73      58
  60      75      60
  58      77      62
  56      79      64
  54      81      66
  52      83      68
  50      85      70
  48      87      72
  46      89      74
  40      95      80

Where the values for z=30 through z=75 (exclusive of the endpoints) satisfy all your criteria, allowing MBC to be anywhere from 25 to 60 as possibilities.


  Posted by Charlie on 2004-06-11 13:10:59
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