Question

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. The angles $(6x - 23)^{\circ}$ and $(4x + 11)^{\circ}$ are vertical angles, so we set up the equation $6x-23 = 4x + 11$.

Step2: Solve the equation for x

Subtract $4x$ from both sides: $6x-4x-23=4x - 4x+11$, which simplifies to $2x-23 = 11$. Then add 23 to both sides: $2x-23 + 23=11 + 23$, getting $2x=34$. Divide both sides by 2: $x=\frac{34}{2}=17$.

Answer:

C. 17