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Math Help - If measurement of arc ST = 71 degrees, calculate m<XST?

  1. #1
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    If measurement of arc ST = 71 degrees, calculate m<XST?

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

    picture:

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

    answers:
    a.) 35.5 degrees
    b.) 54.5 degrees
    c.) 71 degrees
    d.) 109 degrees
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  2. #2
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    Draw radii from R to S and from R to T. That gives a quadrilateral, XSRT, which has angle sum 360 degrees. Since the lines are tangent to the circle, angles RSX and RTX measure 90 degrees. Since the arc has measure 71 degrees, so does angle SRT. So the remaining angle, SXT, has measure 360- 90- 90- 71.
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