Question

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

Explanation:

Step1: Recall tangent - radius property

A tangent to a circle is perpendicular to the radius at the point of tangency. So, $\angle M = 90^{\circ}$.

Step2: Use angle - sum property of a triangle

In $\triangle LMN$, we know that the sum of the interior angles of a triangle is $180^{\circ}$. Let $\angle N=66^{\circ}$, $\angle M = 90^{\circ}$, and $\angle L=x$. Then $x + 90^{\circ}+66^{\circ}=180^{\circ}$. Solving for $x$ gives $x=180^{\circ}-(90^{\circ} + 66^{\circ})=24^{\circ}$.

Answer:

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