Question

LM is tangent to ⊙N at point M. Circle N is shown. Line segment N M is a radii. Line segment L M is a tangent and it intersects with the circle at point M. A line is drawn from point L to point N to form a triangle. Angle L N M is 66 degrees. Determine the following angle measures. m∠M = ° m∠L = °

Answer 1

Answer:

m∠M = 90°

m∠L = 24°

Step-by-step explanation:

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Answer 2

Given :

A circle with center N

∠$LNM = 66^{o}$

To find:

∠$LMN$ and ∠$NLM$

Solution:

If a tangent is drawn through the circumference of the circle that intersect the circle at some point, then, the radius drawn to the foot of the tangent makes an angle of $90^{o}$ with the tangent.

According to the question, tangent $LM$ intersects the circle with center $N$, hence, angle ∠$LMN$ or ∠$M = 90^{o}$.

Now,

According to angle sum property of triangle, we have

∠$LNM$ $+$ ∠$LMN$ $+$ ∠$NLM =180^{o}$

In Δ$LMN$ , we have ∠$LNM = 66^{o}$ and ∠$LMN = 90^{o}$

Therefore,

$66^{o}+ 90^{o}+$ ∠$NLM=180^{o}$   $;$ $or$

∠$NLM = 24^{o}$

Final answer:

Hence, the value of ∠$LMN=90$° and ∠$NLM=24$°.