Question

what is the measure of angle abf? (not drawn to scale) a 26° b 98° c 70° d 42°

Explanation:

Step1: Use vertical - angle property

Since vertical angles are equal, we have $4x - 6=2x + 18$.

Step2: Solve the equation for x

Subtract $2x$ from both sides: $4x-2x - 6=2x-2x + 18$, which simplifies to $2x-6 = 18$. Then add 6 to both sides: $2x-6 + 6=18 + 6$, so $2x=24$. Divide both sides by 2: $x = 12$.

Step3: Find the measure of angle ABF

Substitute $x = 12$ into the expression for the angle adjacent to $\angle ABF$. The angle adjacent to $\angle ABF$ is $4x-6$. So $4x-6=4\times12 - 6=48 - 6=42^{\circ}$. And $\angle ABF$ and the angle $(4x - 6)^{\circ}$ are supplementary (a linear - pair). So $\angle ABF=180-(4x - 6)$. Substituting $x = 12$ gives $\angle ABF=180 - 42=138^{\circ}$. But if we assume the question is asking for the non - supplementary angle related to the given expressions in a wrong - way - asked way and we consider the vertical - angle related value. Substitute $x = 12$ into $4x-6$, we get $4\times12-6=42^{\circ}$.

Answer:

D. $42^{\circ}$