the diagram below shows three intersecting lines. what is the value of x? a 6 b 10.2 c 17 d 19.2

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $6x - 23=4x + 11$.

Step2: Isolate the variable terms

Subtract $4x$ from both sides: $6x-4x - 23=4x-4x + 11$, which simplifies to $2x-23 = 11$.

Step3: Isolate the variable

Add 23 to both sides: $2x-23 + 23=11 + 23$, getting $2x=34$.

Step4: Solve for x

Divide both sides by 2: $\frac{2x}{2}=\frac{34}{2}$, so $x = 17$.

Answer:

C. 17