Question

If m∠NKJ=8x+2 and m∠LKM=3x+5 , what is m∠NKM?

Answer 1

If m∠NKJ =8x+2 and m∠LKM=3x+5 , what is m∠NKM?

KM − → bisects ∠NKL so m∠NKM = m∠LKM

m∠NKJ + 2(m∠LKM)= 180

8x+2 + 2(3x+5) = 180

8x+2 + 6x + 10 = 180

14x + 12 = 180

14x = 168

x = 12

m∠NKM = m∠LKM = 3x+5 = 3(12) + 5 = 41

Answer:

b. 41

Answer 2

check the picture below.

as you see in the picture, all 4 angles add up to 180°, and since we know that KM is an angle bisector to ∡NKL, then that simply means ∡NKM = ∡LKM.

$\bf \stackrel{\measuredangle NKJ}{8x+2}~~+~~\stackrel{\measuredangle LMK}{3x+5}~~+~~\stackrel{\measuredangle NKM}{3x+5}=180\\\\\\14x+12=180\implies 14x=168\implies x=\cfrac{168}{14}\implies x=12\\\\\\\stackrel{\measuredangle NKM}{3x+5}\implies 3(12)+5\implies 41$