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

Part 1)

Part 2)

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

Part 2) Find the measure of angle PMN

we know that

---> by angle addition postulate

we have

substitute

Applying the perpendicular tangent theorem, the missing angles are:

m∠QML = 90°

m∠PMN = 63°

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.

Based on the perpendicular tangent theorem,

m∠QML = m∠QMN = 90°

m∠QML = 90°

m∠PMN = 90° - 27°

m∠PMN = 63°

Learn more about the perpendicular tangent theorem on:

link

a² + b²= c²

24² + 7² = c²

c= 25