Question

overline{lm} is tangent to odot n at point m. determine the following angle measures. mangle m=square^{circ} mangle l=square^{circ}

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

Answer:

\( m\angle M = \boldsymbol{90}^\circ \)
\( m\angle L = \boldsymbol{24}^\circ \)