Question

question 4 6 pts in the diagram below a. if j || k and n is a transversal, what is the measure of angle 1? ____

Explanation:

Step1: Use vertical - angle property

Since vertical angles are equal, the angle with measure $(4x - 9)^{\circ}$ and the angle with measure $(2x+6)^{\circ}$ are vertical angles. So, $4x−9 = 2x + 6$.

Step2: Solve the equation for $x$

Subtract $2x$ from both sides: $4x-2x−9=2x - 2x+6$, which simplifies to $2x−9 = 6$. Then add 9 to both sides: $2x-9 + 9=6 + 9$, giving $2x=15$, and $x = 7.5$.

Step3: Find the measure of one of the angles

Substitute $x = 7.5$ into $(2x + 6)^{\circ}$. We get $2\times7.5+6=15 + 6=21^{\circ}$.

Step4: Use the property of parallel lines

Since $j\parallel k$ and $n$ is a transversal, the angle adjacent to $\angle1$ and the angle with measure $(2x + 6)^{\circ}$ are supplementary. Let the angle adjacent to $\angle1$ be $\alpha$. So $\alpha+(2x + 6)=180$. Since $2x + 6 = 21$, then $\alpha=180 - 21=159^{\circ}$.

Step5: Find the measure of $\angle1$

$\angle1=180 - 123=57^{\circ}$ (because $\angle1$ and the angle adjacent to it are supplementary).

Answer:

$57^{\circ}$