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Two angles∠3 and ∠5 are each supplementary to ∠4. If m∠5 is 78°, what is m∠3?

  1. Sep 6, 2009 #1
    Two angles∠3 and ∠5 are each supplementary to ∠4. If m∠5 is 78°, what is m∠3?

    Two angles∠3 and ∠5 are each supplementary to ∠4. If m∠5 is 78°, what is m∠3?

    A) 102°
    B) 2°
    C) 78°
    D) 90°
    E) 180°


    If two angles are supplements, their sum is 180 degrees.

    Algebraic solution:
    measure ∠5 = 78 degrees
    measure ∠4 = x (we do not know the measure of this angle yet, so it's x)

    So: 78 + x = 180 degrees

    ^^[because these angles are supplements, we know they have to equal 180 degrees]

    If you solve that you find out that x, or measure ∠4, is 102 degrees. Check that by doing 78 + 102 = 180.

    Since ∠3 is also supplementary to angle 4, ∠3 = ∠5

    Which means ∠3 is 78 degrees.


    We have discovered:

    Measure ∠4 = 102 degrees
    Measure ∠5 = 78 degrees
    Measure ∠3 = 78 degrees

    Final answer is C) 78°
     
    Last edited: Sep 6, 2009
  2. jcsd
  3. Sep 6, 2009 #2

    tiny-tim

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    Hi Leo34005! :smile:

    This is very long-winded …

    why not just say that, from that definition, there is a unique supplementary angle to any angle (in this case, ∠4), so any two supplementary angles must be equal? :wink:
     
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