Question

the m∠6=(11x + 8)° and m∠7=(12x - 4)°. what is the measure of ∠4? o m∠4 = 40° o m∠4 = 48° o m∠4 = 132° o m∠4 = 140°

Explanation:

Step1: Set up equation for vertical - angles

Since $\angle6$ and $\angle7$ are vertical - angles, they are equal. So, $11x + 8=12x - 4$.

Step2: Solve for $x$

Subtract $11x$ from both sides: $8=x - 4$. Then add 4 to both sides, we get $x = 12$.

Step3: Find the measure of $\angle6$

Substitute $x = 12$ into the expression for $\angle6$: $m\angle6=11x + 8=11\times12 + 8=132 + 8=140^{\circ}$.

Step4: Use corresponding - angles relationship

$\angle4$ and $\angle6$ are corresponding angles. Corresponding angles formed by parallel lines and a transversal are equal. So $m\angle4=m\angle6 = 140^{\circ}$.

Answer:

$m\angle4 = 140^{\circ}$