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

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°

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: