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    Hi, I was just doing some of the GCSE to A level transition work that I was set and I was wondering if anyone would be able to explain a question to me. If possible, could you give me the reasoning behind why the answer is what it is?

    The question is to find the missing angles i, k and j and the diagram is here: http://tinypic.com/view.php?pic=2s8g...9#.WXjkB73TXqA (sorry if image quality is terrible)

    Thank you
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    Have a look at: http://www.bbc.co.uk/education/guide...tfr/revision/4 (circle theorem)

    and note that the two lines are parallel.
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    (Original post by Math12345)
    Have a look at: http://www.bbc.co.uk/education/guide...tfr/revision/4 (circle theorem)

    and note that the two lines are parallel.
    I understand how to work out k, but not i or j. Which rule do you use for the parallel lines? Is it co-interior angles or something?
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    (Original post by Coco_Monkey)
    I understand how to work out k, but not i or j. Which rule do you use for the parallel lines? Is it co-interior angles or something?
    Yes, co-interior angles is right
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    (Original post by Coco_Monkey)
    I understand how to work out k, but not i or j. Which rule do you use for the parallel lines? Is it co-interior angles or something?
    Because the lines are parallel, j+72=180

    Draw a line through the centre of the circle perpendicular to the parallel lines.

    What can you say about the angles (i, 72) and (j, k) now?
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    (Original post by Math12345)
    Yes, co-interior angles is right
    Well, I thought that meant that the angles next to eachother would add to 180? But the answer sheet says that i is 72 and j is 108 (so the ones which are next to eachother are equal). Or am I an idiot and the ones next to eachother are equal?
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    (Original post by Coco_Monkey)
    Well, I thought that meant that the angles next to eachother would add to 180? But the answer sheet says that i is 72 and j is 108 (so the ones which are next to eachother are equal). Or am I an idiot and the ones next to eachother are equal?
    Circle theorem shows that k+72=180 so k=108
    Using co-interior angles i+k=180 i.e i+108=180 so i=72.
    Similarly j=108 since 180-72=108 (you can use either circle theorem or co-interior angles here)
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    (Original post by Coco_Monkey)
    Well, I thought that meant that the angles next to eachother would add to 180? But the answer sheet says that i is 72 and j is 108 (so the ones which are next to eachother are equal). Or am I an idiot and the ones next to eachother are equal?
    j = 108 because of the parallel lines.

    I and j are opposite angles in a cyclic quadrilateral so we know ....
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    Oh, I see now. I am an absolute idiot. Thanks everyone for helping me with maths and stuff. Not 100% sure how to thank you properly!
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    (Original post by RogerOxon)
    Because the lines are parallel, j+72=180

    Draw a line through the centre of the circle perpendicular to the parallel lines.

    What can you say about the angles (i, 72) and (j, k) now?
    There is no need to add an additional line as there is a cyclic quadrilateral ...
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    (Original post by Muttley79)
    There is no need to add an additional line as there is a cyclic quadrilateral ...
    The simplest way of doing this will vary with what the OP knows. I was just trying to show the symmetry.
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    (Original post by RogerOxon)
    The simplest way of doing this will vary with what the OP knows. I was just trying to show the symmetry.
    The symmetry only exists because of the cyclic quadrilateral ,,,
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    (Original post by Muttley79)
    The symmetry only exists because of the cyclic quadrilateral ,,,
    That's not how I see it, but whatever works. To me, symmetry is the simpler concept.
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    (Original post by RogerOxon)
    That's not how I see it, but whatever works. To me, symmetry is the simpler concept.
    You would only get a mark for stating the relevant property of a cyclic quadrilateral - symmetry would not get you the mark.
 
 
 
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