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Math Help - Calculate the angles

  1. #1
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    Calculate the angles

    Ok I can see how angle B is 80 degrees. Thats all I can solve on my own hand right now. I wonder If you can explain and help me notice other obvious things with the problem.



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  2. #2
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    Quote Originally Posted by kevin3000 View Post
    Ok I can see how angle B is 80 degrees. Thats all I can solve on my own hand right now. I wonder If you can explain and help me notice other obvious things with the problem.




    HI

    Did u mean these three angles , \angle ACB , \angle CAB and \angle ABC .

    If so , you are correct by saying \angle ABC is 80^o .

    Let D be another point intersecting the circle ,

    since ABCD is a cyclic quadrilateral , it should be obvious that
    \angle ACB=180-120

    Then you can finish off the last one .
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  3. #3
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    Quote Originally Posted by mathaddict View Post
    HI

    Did u mean these three angles , \angle ACB , \angle CAB and \angle ABC .

    If so , you are correct by saying \angle ABC is 80^o .

    Let D be another point intersecting the circle ,

    since ABCD is a cyclic quadrilateral , it should be obvious that
    \angle ACB=180-120

    Then you can finish off the last one .
    But where is the point D ?
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  4. #4
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    Angles in the Same Segment

    Hello kevin3000
    Quote Originally Posted by kevin3000 View Post
    Ok I can see how angle B is 80 degrees. Thats all I can solve on my own hand right now. I wonder If you can explain and help me notice other obvious things with the problem.
    You say that you can see how \angle ABC = 80^o. You are right, and the reason that it's equal to the marked angle of 80^o is that they are both subtended by the arc AC.

    We say that angles like this are Angles in the Same Segment - and they're equal.

    (When you divide a circle into two by a chord you get two segments - the bigger one is the major segment, and the smaller one is the minor segment. Here the chord is AC, and the 80^o angle and \angle ABC are both in its major segment.)

    Well now, can you spot the arc that is subtending the marked 40^o angle? It is the arc BC. And this arc also subtends \angle BAC. So these angles are also equal - they're in the major segment of the chord BC. So \angle BAC = 40^o.

    I'm sure you know how to find the third angle of the triangle, \angle ACB, so I'll leave it up to you.

    Grandad
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