Question

LN is tangent to circle o at point M and QM is a diameter. Determine the measure of the following angles.
The measure of QML is degrees
The measure of ZPMN is degrees.
270

Answer 1

Answer:

Part 1) $m\angle QML=90^o$

Part 2) $m\angle PMN=63^o$

Step-by-step explanation:

The complete question in the attached figure

Part 1) Find the measure of angle QML

we know that

According to the Perpendicular Tangent Theorem, tangent lines are always perpendicular to a circle's radius at the point of intersection

so

radius OM is perpendicular to LN at point M

therefore

$m\angle QML=90^o$

Part 2) Find the measure of angle PMN

we know that

$m\angle QMN=m\angle QMP+m\angle PMN$ ---> by angle addition postulate

we have

$m\angle QMN=90^o$

$m\angle QMP=27^o$

substitute

$90^o=27^o+m\angle PMN$

$m\angle PMN=90^o-27^o=63^o$

Answer 2

Applying the perpendicular tangent theorem, the missing angles are:

m∠QML = 90°

m∠PMN = 63°

What is the Perpendicular Tangent Theorem?

The Perpendicular Tangent Theorem states that tangent lines are perpendicular to the radius of a circle at the point where they intersect, forming a right angle.

• Thus:

Based on the perpendicular tangent theorem,

m∠QML = m∠QMN = 90°

• Thus:

m∠QML = 90°

m∠PMN = 90° - 27°

m∠PMN = 63°

Learn more about the perpendicular tangent theorem on:

https://brainly.com/question/9892082