## 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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2021-11-10T13:44:23+00:00
2021-11-10T13:44:23+00:00 2 Answers
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## Answers ( )

Answer:The measure of ∠QML is

90°The measure of ∠PMN is

117°Step-by-step explanation:In circle O:

∵ 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°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: