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19 February, 21:01

If YU=YV, ST=16, mQS=34, and mRT=98, find each measure.

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  1. 19 February, 21:18
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    Answer: QR=8; QU=76

    Measure of the arc ST=114°

    Measure of the arc QR=114°

    Measure of the arc XT=57°

    Step-by-step explanation:

    Given that,

    YU=YV

    ST=16

    mQS=34

    mRT=98

    We will use pythagoras theorem,

    QR=8

    QU=76

    QR=ST

    Since they span the same arc, let the arc be x.

    360 - QS - RT = QR + ST

    Recall that QR=ST

    360 - 34 - 98 = x + x

    228 = 2x

    Divide both side by 2

    X = 228/2

    X=114°

    Therefore, the measure of the arc ST and the arc QR=114°

    Measure of span of arc XT will be:

    = 1/2 * (arc ST)

    = 1/2 * 114

    = 57°
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