Question

Show me how to get this answer show your work

Answer 1

The measure of angle MKJ is equal to the sum of angles MKL and JKL by the angle addition postulate. that means
2x+10 + 3x-5=80. solve for x...

5x+5=80
5x=75
x=15

now plug 15 in n for x in both angles. you'll see that the measure of both angles is 40. since segment KL cuts the big angle exactly in half, it is the angle bisector. your checked answer is the right one.

Answer 2

We know that angle MKJ is comprised of angle MKL and angle LKJ. That means if we add MKL and LKJ, we should get 80 degrees, which is the measure of angle MKJ.

$MKL + LKJ= MKJ \implies \\ 2x+10+3x-5=80 \implies \\ 5x+5=80 \implies\\ 5x=75 \implies \\ x=15$

So, we know that our x is 15. That is not enough to tell whether KL is an angle bisector, because we have to evaluate both MKL and LKJ with x=15, so:

$MKL=2(15)+10 = 40\\ LKJ=3*15-5=40$

So we see that these two angles are actually bisectors, and the third question best describes this phenomenon.