Question

state the angle pair and then find x in the figure below \\( \angle 4 = 14 x \\) and \\( \angle 5 = 3 x + 44 \\).

Explanation:

Step1: Identify the angle pair

$\angle4$ and $\angle5$ are alternate - interior angles. When two parallel lines are cut by a transversal, alternate - interior angles are congruent. So, $\angle4=\angle5$.

Step2: Set up the equation

Since $\angle4 = 14x$ and $\angle5=3x + 44$, we have the equation $14x=3x + 44$.
Subtract $3x$ from both sides: $14x-3x=3x + 44-3x$.
This simplifies to $11x=44$.

Step3: Solve for $x$

Divide both sides of the equation $11x = 44$ by $11$: $x=\frac{44}{11}$.

Answer:

$x = 4$