Question

$\overline{lm}$ is tangent to $\odot n$ at point m.
determine the following angle measures.
$m\angle m=\square^\circ$
$m\angle l=\square^\circ$
the circle $\odot n$ has a central angle $\angle mnl = 66^\circ$

Explanation:

Step1: Identify tangent-radius angle

A tangent to a circle forms a right angle with the radius at the point of tangency. So $\angle LMN = 90^\circ$.

Step2: Calculate $\angle L$ using triangle sum

The sum of angles in a triangle is $180^\circ$. In $\triangle LMN$, we know $\angle MNL = 66^\circ$ and $\angle LMN = 90^\circ$.
$m\angle L = 180^\circ - 90^\circ - 66^\circ = 24^\circ$

Answer:

$m\angle M = 90^\circ$
$m\angle L = 24^\circ$