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Exterior angle of a triangle?

  1. Dec 4, 2016 #1
    1. The problem statement, all variables and given/known data
    upload_2016-12-4_12-43-8.png

    It looks as if 50 degrees is an external angle of the triangle.So it should be greater than the two opposite interior angles (i.e x and the other one). But book tells a different answer. Somebody please guide me.


    Zulfi.

    2. Relevant equations
    No eq. Rule: Exterior angle of a triangle is greater than the two opposite interior angles of atriangle

    3. The attempt at a solution
    50 degree must be greater than x because it is an exterior angle of a triangle.

    Somebody please guide me.

    Zulfi.
     
  2. jcsd
  3. Dec 4, 2016 #2
    Why do think 50° is an exterior angle ?
    Is it contained between two sides of the triangle ?
     
    Last edited: Dec 4, 2016
  4. Dec 4, 2016 #3

    Nidum

    User Avatar
    Science Advisor
    Gold Member

    Does the problem statement tell you what type of triangle it is ?

    One particular type of triangle would let you get your answer by inspection . What type would that be ?
     
    Last edited: Dec 4, 2016
  5. Dec 4, 2016 #4
    Hi,
    Thanks. Question does not say anything about the triangle. It says that l & k are parallel lines.
    I got a explanation of exterior angle from a website:

    At each vertex of a triangle, an exterior angle of the triangle may be formed by extending ONE SIDE of the triangle. See picture below.

    Its now clear to me whats an exterior angle
    exterior1.gif

    I have one another question:
    Is the other angle within the triangle, in my question (opposite to x) equals to 50 because its a transversal cutting two parallel lines?
    Plz guide me.

    Zulfi.
     
  6. Dec 4, 2016 #5

    Nidum

    User Avatar
    Science Advisor
    Gold Member

    Post removed pro tem .
     
  7. Dec 4, 2016 #6
    Hi,
    <One particular type of triangle would let you get your answer by inspection . What type would that be ?>
    Equilateral. In that case x would be 60 which is not same as 50.

    Zulfi.
     
  8. Dec 4, 2016 #7
    Ok I tell the answer now but first I want to know the reason from you why you think so (state some theorem, law, axiom ... that prompted you to think so).
     
  9. Dec 4, 2016 #8
    Then the angle formed by the transversal will also change, So don't think about a special case of the triangle.
     
  10. Dec 4, 2016 #9
    Hi,
    Thanks for your reply.


    Sorry it not adding the picture. I would ask my question in another post.


    Zulfi.
     
  11. Dec 4, 2016 #10
    Hi,
    In the above picture, is y equal to 50?
    Zulfi.
     
  12. Dec 4, 2016 #11
    Hi,
    In the following picture, is y equal to 50?
    upload_2016-12-4_19-1-34.png
    Zulfi.
     
    Last edited by a moderator: Dec 4, 2016
  13. Dec 4, 2016 #12
    I can't provide you direct answer because the last time I did so, a mentor warned me not to do so.

    But I can say if you are right or wrong, if you tell me what do you think about your question with proper reasoning, i.e tell me whether y = 50 or not and justify it.
    You might want to use the 'property of angles on the alternate sides of transversal' .
     
    Last edited: Dec 4, 2016
  14. Dec 4, 2016 #13

    Mark44

    Staff: Mentor

    Your picture is confusing. Is angle y the interior angle that is marked?
     
  15. Dec 6, 2016 #14
    Hi,
    <Is angle y the interior angle that is marked?>
    Yes.
    <But I can say if you are right or wrong, if you tell me what do you think about your question with proper reasoning, i.e tell me whether y = 50 or not and justify it.>
    Actually i already told you about the traversal. Now i am writing the rule:
    If a pair of lines is cut by a traversal that is not perpendicular to the parallel lines then:
    Four acute angles are equal & four obtuse angles are equal. That's i am thinking that 'y' which i have marked as the interior angle of triangle is equal to 50.
    Zulfi.
     
  16. Dec 6, 2016 #15
    Yes you are correct. The rule you stated, in short is "Interior angles on the opposite sides of the transversal are equal.".
     
  17. Dec 6, 2016 #16

    Mark44

    Staff: Mentor

    In that case, angle y is 50°.
     
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