Question

ray MP bisects angle LMN. the measure of angle LMP is 2x+12, and the measure of angle LMN is x2-x. what is the measure of angle LMN

Answer 1

∠LMP=∠PMN and ∠LMN=∠LMP+∠PMN.

2x+12=∠PMN and x²-x=2x+12+2x+12=4x+24.

So x²-x=4x+24, x²-5x-24=0, (x-8)(x+3)=0.

Therefore x=8 or -3.

∠LMP=∠PMN=2x+12=28 or 6 and ∠LMN=56 or 12.