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  1. #1
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    Geometry Help

    If measurement of arc ST = 71 degrees, calculate m<SXT?

    picture:

    http://i121.photobucket.com/albums/o...oryz/002-8.jpg

    answers:
    a.) 54.5 degrees
    b.) 71 degrees
    c.) 109 degrees
    d.) 142 degrees
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  2. #2
    Super Member Matt Westwood's Avatar
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    Are you allowed to use the fact that the internal angles of a quadrilateral add up to 360 degrees?

    If so, note that RSXT is a quadrilateral whose angles you know all of except for the one you are being asked to find.
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  3. #3
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    Quote Originally Posted by Muneeb View Post
    If measurement of arc ST = 71 degrees, calculate m<SXT?
    ...
    m < SXT

    The picture does not identify "m"
    I do not know what "m" is or how you could possibly
    detemine whether it is greater, equal or less that "sxt"

    Could you elaborate?
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  4. #4
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    Grandad's Avatar
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    Hello Muneeb
    Quote Originally Posted by Muneeb View Post
    If measurement of arc ST = 71 degrees, calculate m<SXT?

    picture:

    http://i121.photobucket.com/albums/o...oryz/002-8.jpg

    answers:
    a.) 54.5 degrees
    b.) 71 degrees
    c.) 109 degrees
    d.) 142 degrees
    You need two facts here:

    • The angle between a tangent to a circle and the radius at the point of contact is 90^o.


    • The angles of a quadrilateral add up to 360^o.

    So \angle XSR = \angle XTR =90^o.

    You are given that the arc ST subtends an angle of 71^o at the centre of the circle. So \angle SRT = 71^o.

    So \angle SXT = 360 - (90+90+71) = 109^o

    Grandad
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  5. #5
    Super Member Matt Westwood's Avatar
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    Quote Originally Posted by aidan View Post
    m < SXT

    The picture does not identify "m"
    I do not know what "m" is or how you could possibly
    detemine whether it is greater, equal or less that "sxt"

    Could you elaborate?
    In this context "m < SXT" means "the measure of the angle SXT".

    I'd normally write it \angle SXT but I appreciate different notation is used in various places.
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