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Measure that angle (Posted on 2002-06-18) Difficulty: 5 of 5
Given that:
  • ABC is an isosceles triangle in which
        AB = AC
  • The lengths of the following segmets are equal:
        AD
        DE
        EC
        BC
    Find the measure of angle A.
  • See The Solution Submitted by vohonam    
    Rating: 4.2000 (20 votes)

    Comments: ( Back to comment list | You must be logged in to post comments.)
    re(2): Oh wait - I gottit! | Comment 18 of 59 |
    (In reply to re: Oh wait - I gottit! by Cheradenine)

    Okay. I guess you're okay with BDE is "2a"? Well, we know angle AED is "a". And this angle is bisected by the vertical line in the picture, so the line AB must be "a/2" from the vertical, either side of the line. Now, if we draw a vertical line down through D we have just shown that DB must be "a/2" from the vertical - as the full angle BDE is "2a", this means the line DE must be "2a"-"a/2" from the vertical - i.e. "3a/2"
      Posted by Nick Reed on 2002-06-19 01:58:03

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