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 Another Point In A Square (Posted on 2004-06-11)
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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