Question

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

Answer 1

Answer:

Pmn is 63

Step-by-step explanation:

Answer 2

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°