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In triangle JKL, JL is extended through point L to point M. If \( m\angle KLM = (8x - 16)^\circ \), and m... [Complete the information to proceed with the question.]

Answer :

Final answer:

In this case, the measure of angle KLM is approximately 8(14.46) - 16 = 116.68 degrees.

Explanation:

To find the measure of angle KLM, we need to use the fact that the sum of the angles in a triangle is always 180 degrees.

In triangle JKL, we have three angles: ∠JKL, ∠LJK, and ∠KLM.

m∠LJK = (2x+2) degrees

m∠KLM = (8x-16) degrees

m∠JKL = (3x+6) degrees

To find the measure of angle KLM, we can add the three angles and set the sum equal to 180:

(2x+2) + (8x-16) + (3x+6) = 180

Now, we can simplify and solve the equation for x:

2x + 8x + 3x + 2 - 16 + 6 = 180

13x - 8 = 180

13x = 180 + 8

13x = 188

x = 188/13

x = 14.46

Therefore, the measure of angle KLM is approximately 8(14.46) - 16 = 116.68 degrees.

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Your question is incomplete, but most probably the full question was:

In ΔJKL, [tex]\overline{JL}[/tex] is extended through point L to point M, [tex]\text{m}\angle LJK = (2x+2)^{\circ} \text{m}\angle LJK=(2x+2)^{\circ}[/tex], [tex]\text{m}\angle KLM = (8x-16)^{\circ}m∠KLM=(8x−16)^{\circ}[/tex], and [tex]\text{m}\angle JKL = (3x+6)^{\circ}m∠JKL=(3x+6)^{\circ}[/tex]. Find [tex]\text{m}\angle[/tex] KLM.m∠KLM.

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