class work: monday 9/8/25
1) a c b (ac=6x+2, cb=x+1, ab=52) x=____ ac=____
2) if e lies between b and c then ____
3) if d is in the interior of ∠abe then ____
(diagram: v, a, b, c; ∠avc=72°, ∠aub=5x+5, ∠bvc=8x+2) find x=____, m∠aub=____, m∠bvc=____

Question

Accepted Answer

### Problem 1: Segment Lengths
# Explanation:
## Step1: Set up the equation
Since $ AC + CB = AB $, we have $ (6x + 2) + (x + 1) = 52 $.
Simplify: $ 7x + 3 = 52 $.
## Step2: Solve for $ x $
Subtract 3 from both sides: $ 7x = 52 - 3 = 49 $.
Divide by 7: $ x = \frac{49}{7} = 7 $.
## Step3: Find $ AC $
Substitute $ x = 7 $ into $ AC = 6x + 2 $: $ AC = 6(7) + 2 = 42 + 2 = 44 $.
# Answer:
$ x = 7 $, $ AC = 44 $

### Problem 2: Point Between Segments
# Brief Explanations:
If $ E $ lies between $ B $ and $ C $, then by the segment addition postulate, $ BE + EC = BC $ (or $ BB + EC = BC $ if there's a typo, but likely $ BE + EC = BC $).
# Answer:
$ BE + EC = BC $ (or appropriate segment addition based on correct labels)

### Problem 3: Angle Addition (with $ \angle AVC = 72^\circ $, $ \angle AUB = 5x + 5 $, $ \angle BVC = 8x + 2 $)
# Explanation:
## Step1: Set up the angle equation
Since $ \angle AUB + \angle BVC = \angle AVC $, we have $ (5x + 5) + (8x + 2) = 72 $.
Simplify: $ 13x + 7 = 72 $.
## Step2: Solve for $ x $
Subtract 7: $ 13x = 72 - 7 = 65 $.
Divide by 13: $ x = \frac{65}{13} = 5 $.
## Step3: Find $ m\angle AUB $
Substitute $ x = 5 $: $ 5(5) + 5 = 25 + 5 = 30^\circ $.
## Step4: Find $ m\angle BVC $
Substitute $ x = 5 $: $ 8(5) + 2 = 40 + 2 = 42^\circ $.
# Answer:
$ x = 5 $, $ m\angle AUB = 30^\circ $, $ m\angle BVC = 42^\circ $

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QUESTION IMAGE

Question

Explanation:

Problem 1: Segment Lengths

Step1: Set up the equation

Step2: Solve for \( x \)

Step3: Find \( AC \)

Step1: Set up the angle equation

Step2: Solve for \( x \)

Step3: Find \( m\angle AUB \)

Step4: Find \( m\angle BVC \)

Answer:

Problem 2: Point Between Segments