Question

lm is tangent to ⊙n at point m. determine the following angle measures. m∠m = □° m∠l = □°

Explanation:

Step1: Find \( m\angle M \)

A tangent to a circle is perpendicular to the radius at the point of tangency. So, \( \overline{LM} \perp \overline{NM} \), which means \( m\angle M = 90^\circ \).

Step2: Find \( m\angle L \)

In triangle \( LMN \), we know \( m\angle M = 90^\circ \) and \( m\angle N = 66^\circ \). The sum of angles in a triangle is \( 180^\circ \). Let \( m\angle L = x \). Then:
\[
x + 90^\circ + 66^\circ = 180^\circ
\]
\[
x + 156^\circ = 180^\circ
\]
\[
x = 180^\circ - 156^\circ = 24^\circ
\]
So, \( m\angle L = 24^\circ \).

Answer:

\( m\angle M = 90^\circ \), \( m\angle L = 24^\circ \)