Question

∠6 and ∠7 form a linear pair. twice the measure of ∠6 is twelve more than four times the measure of ∠7. find the measure of each angle. m∠6 = m∠7 =

Explanation:

Step1: Set up equations

Let $m\angle7 = x$ and $m\angle6=y$. Since $\angle6$ and $\angle7$ form a linear - pair, $y + x=180$. Also, given that $2y=4x + 12$, or $y = 2x+6$.

Step2: Substitute $y$ into the linear - pair equation

Substitute $y = 2x + 6$ into $y+x=180$. We get $(2x + 6)+x=180$.
Combining like terms: $3x+6 = 180$.
Subtract 6 from both sides: $3x=180 - 6=174$.
Divide both sides by 3: $x=\frac{174}{3}=58$.

Step3: Find the measure of $\angle6$

Substitute $x = 58$ into $y+x=180$, so $y=180 - 58 = 122$.

Answer:

$m\angle7 = 58^{\circ}$, $m\angle6 = 122^{\circ}$