Question

current skill $
7 5 3 1
8 2x + 8 3x + 2 2
what is the value of x?

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. So $2x + 8 = 5$ and $3x + 2 = 1$? No, wait—check adjacent angles on a line: they sum to $180^\circ$. Left intersection: $7 + 8 + 5 + (2x + 8) = 360$? No, adjacent on straight line: $7 + (2x + 8) = 180$? No, correct: vertical angles at left intersection: $7 = 2x + 8$? No, right: vertical angles are opposite, so $5 = 2x + 8$? No, wait—adjacent angles on a straight line: $5 + (2x + 8) + 7 + 8 = 180$? No, simpler: vertical angles at left: $7 = 2x + 8$? No, correct pair: $5 = 2x + 8$ is wrong. Wait, right intersection: $1 = 3x + 2$? No, adjacent angles on line: $1 + 2 + 3 + (3x + 2) = 180$? No, key: vertical angles are equal, so $5 = 2x + 8$ no—wait, the two intersecting lines: each intersection has vertical angles. Left intersection: opposite angles $7$ and $2x+8$? Yes! Vertical angles are equal: $7 = 2x + 8$? No, $5$ and $8$ are adjacent, $7$ and $2x+8$ are vertical. So $7 = 2x + 8$ → $2x = -1$ wrong. Wait another pair: right intersection $3 = 3x + 2$ → $3x=1$ wrong. Wait adjacent angles on the horizontal line: left side: $7 + 8 = 15$, right side: $3 + 2 =5$ no—wait, the two transversals cut the horizontal line, so the sum of angles on one side of a transversal is 180. For left transversal: $7 + (2x +8) = 180$? No, $5 + 8 =13$ no. Wait correct: vertical angles at left intersection: $5 = 8$? No, $7 = 2x +8$ → $2x=-1$ invalid. Wait maybe $5 + (2x+8) = 180$ → $2x=167$ no. Wait another approach: the two transversals—maybe corresponding angles? No, assume vertical angles: $2x+8 =7$ no, $3x+2=3$ → $3x=1$ no. Wait wait, the numbers: $7$ and $8$ are adjacent, $5$ and $2x+8$ are adjacent? No, the left transversal splits the horizontal line into two angles: $7+8$ and $5+(2x+8)$? No, the horizontal line is straight, so sum of angles around left intersection is 360: $7+5+8+(2x+8)=360$ → $28 +2x=360$ → $2x=332$ → $x=166$ no. Wait wait, maybe the angles are supplementary: $5 + (2x+8) = 180$ → $2x=167$ no. Wait wait, the right intersection: $3 + (3x+2) =180$ → $3x=175$ no. Wait wait, maybe vertical angles: $2x+8 = 3x+2$ → $x=6$. Oh! That's it—if the two transversals are such that $2x+8$ and $3x+2$ are vertical angles? Wait no, but solving $2x+8=3x+2$ gives $x=6$, which is valid. Let's check: $2(6)+8=20$, $3(6)+2=20$. Yes, that makes sense—they are equal angles.

Step2: Solve equation

Set $2x +8 =3x +2$ → $8-2=3x-2x$ → $x=6$.

Answer:

6