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In triangle JKL, an angle bisector drawn from vertex K intersects the opposite side at point P.if JKL is 2y+25 and PKL is 8y - 17, what is the measure of JKL.show all of your work.

Respuesta :

Answer:

Therefore,

[tex]\angle JKL=34.08\°[/tex]Step-by-step explanation:

Given:

KP is the angle bisector of ∠ JKL,

∠JKL = 2y + 25

∠ PKL = 8y - 17

To Find:

∠ JKL = ?

Solution:

KP is the angle bisector of ∠ JKL, .. given

Angle bisector divides the angle in two equal parts such that,

[tex]\angle JKL=2\times \angle PKL[/tex]

Substituting the values we get

[tex]2y+25=2(8y-17)[/tex]

Apply Distributive Property we get

[tex]2y+25=2\times 8y-2\times 17=16y-34\\\\16y-2y=34+25=59\\\\14y=59\\\\y=\dfrac{59}{14}=4.54[/tex]

Now substitute y in JKL

[tex]\angle JKL=2 \times 4.54+25=34.08\°[/tex]

Therefore,

[tex]\angle JKL=34.08\°[/tex]

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