Question

LM is tangent to ⊙N at point M.

Determine the following angle measures.

m∠M =
m∠L =

Answer 1

The correct answer is:

m∠M = 90°

m∠L = 24°

Since LM is tangent to ⊙N at point M the above angle measures are as shown.

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Answer 2

LM is tangent to ⊙N at point M.

m∠M =   90°

m∠L =  24°

According to the given figure

Given a circle with center N

ΔLMN is given

According to the given figure we an observe that LM is  a tangent to the circle.

From the property of tangent to the circle we can write that radius of the circle is perpendicular to the tangent of the circle

So from the property of tangent to the circle we can conclude that ∠ NML = ∠ M = 90°

Also ∠ LNM = 66°

From the angle sum property of a triangle

The sum of interior angles of a triangle is 180°

So from ΔLMN  we can write

$\rm \angle MLN + \angle LMN + \angle LNM = 180 \textdegree \\\\ \angle MLN +90\textdegree +66\textdegree = 180 \textdegree \\\\\angle MLN = 180 \textdegree -156\textdegree \\\angle MLN = \angle L = 24\textdegree$

So we can conclude that in  ΔLMN

m∠M =   90°

m∠L =  24°

For more information please refer to the link given below

https://brainly.com/question/1503247