Question

1. which point on a number line is of the distance between - 12 and 8?
2. ∠dmf is bisected by (overrightarrow{mg}) where (mangle dmg=(4x)^{circ}) and (mangle dmf=(2x + 24)^{circ}).

a. draw a sketch of the diagram and label with measurements.
b. solve for x.
c. find (mangle dmg).

1. line segment (kn) is shown where (kr = 16x-3), (rw = wn), (wn = 9x - 3), (br=\frac{1}{2}rw), and (kn = 161).

a. find the value of x.
b. find the length of (overline{kw}).

1. if (k) is the mid - point of (overline{jl}), (jk = 8x + 11) and (kl = 14x-1), find (jl).

Explanation:

Step1: Find distance between - 12 and 8

$8-(-12)=20$, then $\frac{1}{4}\times20 = 5$, $-12 + 5=-7$ (error above, correct: $8-(-12)=20$, $\frac{3}{4}\times20 = 15$, $-12+15 = 3$)

Step2: For 18b, use angle - bisector property $4x=2x + 24$, solve for $x$: $4x-2x=24$, $2x=24$, $x = 12$

Step3: For 18c, substitute $x = 12$ into $m\angle DMG=4x$, $m\angle DMG=4\times12 = 48$

Step4: For 19a, $KR+RW+WN=KN$, $16x-3+(9x - 3)+(9x - 3)=161$, $34x-9 = 161$, $34x=170$, $x = 5$

Step5: For 19b, $RW=WN=9x - 3=9\times5-3 = 42$, $KR=16x - 3=16\times5-3 = 77$, $KW=KR + RW=77 + 42=119$ (error above, correct: $KR = 16x-3=16\times5 - 3=77$, $RW=WN=9x - 3=9\times5-3 = 42$, $KW=KR+RW=77 + 42 = 119$)

Step6: For 20, since $JK = KL$, $8x+11=14x - 1$, $11 + 1=14x-8x$, $6x=12$, $x = 2$, $JL=JK + KL=2(8x + 11)=2(8\times2+11)=2(16 + 11)=50$

Answer:

Question 17: -3
Question 18a: (Sketch not provided in text - should show angle DMF with ray MG bisecting it, labeled with given angle measures)
Question 18b: 12
Question 18c: 48°
Question 19a: 5
Question 19b: 122
Question 20: 50