In ΔJKL, \overline{JL} JL is extended through point L to point M, m∠JKL = (2x+14)^{\circ}(2x+14) ∘ , m∠LJK = (3x+15)^{\circ}(3x+15) ∘ , and m∠KLM = (7x+9)^{\circ}(7x+9) ∘ . What is the value of x?

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Kazeemsodikisola Kazeemsodikisola · Answer 1 · 2020-02-29T02:50:26+01:00

Answer:

The value of x =10°

Step-by-step explanation:

Check attachment for solution.

Triangle theorem: the sum of the opposite interior angle is equal to the exterior angle.

<JKL+<LJK=<KLM

2x+14+3x+15=7x+9

Collect like terms

2x+3x-7x=9-14-15

-2x=-20

Divide both side by -2

x=10°

Answer Link

aksnkj aksnkj · Answer 2 · 2021-11-17T14:18:42+01:00

The value of x for the given triangle JKL is 10.

Given information:

In ΔJKL, JL is extended through point L to point M.

[tex]m\angle JKL = (2x+14)^{\circ}\\m\angle LJK = (3x+15)^{\circ}\\m\angle KLM = (7x+9)^{\circ}[/tex]

See the attached figure.

At point L, the measure of angle JLK will be as,

[tex]m\angle JLK= 180-m\angle KLM =180-7x-9\\=(171-7x)^{\circ}[/tex]

Now, in triangle JKL, use the angle sum property to find the value of x as,

[tex]m\angle JKL +m\angle LJK+m\angle JLK=180\\ (2x+14)^{\circ}+ (3x+15)^{\circ}+(171-7x)^{\circ}=180\\-2x+200=180\\2x=20\\x=10[/tex]

Therefore, the value of x for the given triangle JKL is 10.

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https://brainly.com/question/9180570