SOLUTION: 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

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Question 1151992: 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
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.

From the condition,


    2y + 25 = 2*(8y - 17).


Simplify and solve for y


    2y + 25 = 16y - 34

    25 + 34 = 16y - 2y

    59      = 14y

     y      = 59%2F14.    


The measure of < JKL  is 2y+25 = 2%2A%2859%2F14%29%2B25 = 59%2F7 + 25 = 8 + 3%2F7 + 25 = 333%2F7.     ANSWER


Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
If < JKL+=2y+%2B+25 and < PKL=8y+-17, what is the measure of < JKL
since angle bisector drawn from vertex K, we have
< PKJ= < PKL=8y+-17
< JKL=2* <+PKL


2y+%2B+25=2%2A%288y+-17%29
2y+%2B+25=16y+-34
34%2B+25=16y+-2y
59=14y+
y=59%2F14

< JKL+=2y+%2B+25
< JKL+=2%2859%2F14%29+%2B+25
< JKL+=59%2F7+%2B+25
< JKL+=8%263%2F7+%2B+25
< JKL+=33%263%2F7+