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Angle properties: Angles centered at a point?

  1. Aug 9, 2016 #1
    1. The problem statement, all variables and given/known data
    Find what x is
    bandicam 2016-08-09 20-05-56-722.jpg
    I don't understand what to do with (3x-23).

    2. Relevant equations
    Angles centered at a point: a+b+c+d=360

    https://drtayeb.files.wordpress.com/2011/03/igcse-math-extended.pdf
    (here is a pdf of the textbook, Exercise 4A, 3i.)



    3. The attempt at a solution
    a+b+c+d=360
    45+44=89
    360-89=271
    two angles left to solve for final equation: 3x,x and (3x-23)
    (3x-23)? <- please tell me what to do with this, do you isolate it?
     
  2. jcsd
  3. Aug 9, 2016 #2

    Nidum

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    Clue : Sum the whole lot into an equation for x :

    3x + (3x - 23) + ------- = ??
     
  4. Aug 9, 2016 #3

    ehild

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    There are four angles, a=45, b= x+44, c=3x-23, d=3x. They are expressed in terms of x. Just add the angles, 45 + (x+44) + (3x-23) + (3x) = 360. You get the equation for the unknown x. Collect the like terms and solve for x.
     
  5. Aug 9, 2016 #4
    Thank you ehild, your explanation really helped a lot.

    45+(x+44)+(3x-23)+3x=360
    7x+66=360
    7x=294
    7x/7=294/7
    x=42
     
  6. Aug 9, 2016 #5

    ehild

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    Nice work!
     
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