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anonymous

  • one year ago

Given that m<GHJ is 14 degrees, find m<HIJ.

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  1. anonymous
    • one year ago
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  2. phi
    • one year ago
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    do you know which angle is <GHJ ?

  3. anonymous
    • one year ago
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    yes @phi

  4. phi
    • one year ago
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    Here is the picture

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  5. phi
    • one year ago
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    any idea what the angle <GHJ + < IHJ add up to ? in the picture it's 154 + X (easier to type)

  6. anonymous
    • one year ago
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    That's where I get confused, because there is no actual number for x.

  7. phi
    • one year ago
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    it does not matter what the number is ... the idea is those two angles form a straight line and a straight line is an angle of how many degrees?

  8. anonymous
    • one year ago
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    Oh, I got x=26. I subtracted 154 from 180

  9. phi
    • one year ago
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    yes. we also know the two "marked angles" are equal (that is what the red arcs mean) if we call them Y (for convenience) the 3 angles of the triangle Y+Y+X= 180 and also from the first post 154+X= 180 so we can say 2Y+ X = 154+X or (subtract off X from both sides) 2Y= 154 now you can find Y (i.e. angle HIJ)

  10. anonymous
    • one year ago
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    I got y=77 degrees, thank you for all the help!!

  11. phi
    • one year ago
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    or we could use x=26 and say 2Y+26= 180 2Y= 180-26 2Y= 154 Y= 77

  12. phi
    • one year ago
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    the reasoning was a bit complicated... once people figured it out they said let the < GHJ be called an "exterior angle" and the exterior angle equals the sum of the two opposite angles. that lets you write down <GHJ = 2*<HIJ or 154 = 2 * <HIJ and <HIJ= 77

  13. anonymous
    • one year ago
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    I posted a similar one just now, it's even harder. Your explanation makes sense, thank you again!

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