Question

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.

Answer 1

Therefore,

`\angle JKL=34.08\°`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,

`\angle JKL=2* \angle PKL`

Substituting the values we get

`2y+25=2(8y-17)`

Apply Distributive Property we get

`2y+25=2* 8y-2* 17=16y-34\\\\16y-2y=34+25=59\\\\14y=59\\\\y=(59)/(14)=4.54`

Now substitute y in JKL

`\angle JKL=2 * 4.54+25=34.08\°`

Therefore,

`\angle JKL=34.08\°`