the $m\\angle6=(11x + 8)^{circ}$ and $m\\angle7=(12x - 4)^{circ}$. what is the measure of $\\angle4$…

the $m\\angle6=(11x + 8)^{circ}$ and $m\\angle7=(12x - 4)^{circ}$. what is the measure of $\\angle4$? $m\\angle4 = 40^{circ}$ $m\\angle4 = 48^{circ}$ $m\\angle4 = 132^{circ}$ $m\\angle4 = 140^{circ}$

the $m\\angle6=(11x + 8)^{circ}$ and $m\\angle7=(12x - 4)^{circ}$. what is the measure of $\\angle4$? $m\\angle4 = 40^{circ}$ $m\\angle4 = 48^{circ}$ $m\\angle4 = 132^{circ}$ $m\\angle4 = 140^{circ}$

Answer

Explanation:

Step1: Use vertical - angle property

$\angle6$ and $\angle7$ are vertical angles, so $m\angle6 = m\angle7$. $11x + 8=12x - 4$

Step2: Solve for $x$

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

Step3: Find $m\angle6$

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

Step4: Use corresponding - angle property

$\angle4$ and $\angle6$ are corresponding angles, so $m\angle4=m\angle6$. $m\angle4 = 140^{\circ}$

Answer:

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