geometry

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Rays PQ and QR are perpindicular. Point S lies i the interior of angle PQR. If the measure of the angle SQR=4+7a and the measure of angle SQR=9=4a, find the measure of angle of PQS and angle SQR.

  • geometry -

    angle PQS + angle PQR= 90
    so, 4+7a+9+4a=90
    7a+4a=90-4-9
    11a=77
    a=7

    check:
    PQS= 4+7a
    4+7(7)=53

    PQR= 9+4a
    =9+4(a)=37

    53+37=90

  • geometry -

    angle PQS + angle SQR= 90
    so, 4+7a+9+4a=90
    7a+4a=90-4-9
    11a=77
    a=7

    check:
    PQS= 4+7a
    4+7(7)=53

    SQR= 9+4a
    =9+4(a)=37

    53+37=90

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