Line segment L N is tangent to circle O at point M and QM is a diameter. Circle O is shown. Line segment Q M is a diameter. Line

Question

Line segment L N is tangent to circle O at point M and QM is a diameter.

Circle O is shown. Line segment Q M is a diameter. Line segments P M and Q R are secants. Line segment N L is a tangent and intersects the circle at point M. Angle P M O is 27 degrees and angle M Q R is 42 degrees.

Determine the measure of the following angles.

The measure of ∠QML is degrees.

The measure of ∠PMN is degrees.

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Nevaeh 2 weeks 2021-11-10T13:44:23+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-10T13:45:56+00:00

    Answer:

    The measure of ∠QML is 90°

    The measure of ∠PMN is 117°

    Step-by-step explanation:

    In circle O:

    • MQ is a diameter
    • LN is a tangent to circle O at point M
    • PM and RQ are secants
    • m∠PMO is 27°
    • m∠MQR is 42

    ∵ MQ is a diameter of circle O

    ∵ LN is a tangent to circle O at point M

    – A diameter is perpendicular to a tangent at the point of

     contact between them (one of end-point of the diameter)

    ∴ QM ⊥ LN at point M

    ∴ m∠QML = m∠QMN = 90°

    The measure of ∠QML is 90°

    ∵ m∠PMN = m∠PMO + m∠QMN

    ∵ m∠PMO = 27° ⇒ given

    ∵ m∠QMN = 90° ⇒ proved

    ∴ m∠PMN = 27 + 90

    ∴ m∠PMN = 117°

    The measure of ∠PMN is 117°

    0
    2021-11-10T13:46:05+00:00

    Answer:

    Line segment L N is tangent to circle O at point M and QM is a diameter.

    Circle O is shown. Line segment Q M is a diameter. Line segments P M and Q R are secants. Line segment N L is a tangent and intersects the circle at point M. Angle P M O is 27 degrees and angle M Q R is 42 degrees.

    Determine the measure of the following angles.

    The measure of ∠QML is  

    ✔ 90

    degrees.

    The measure of ∠PMN is  

    ✔ 63

    degrees.

    Step-by-step explanation:

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