Question

in the picture, line a is parallel to line b. m∠2 is 68 less than 5 times m∠6. ∠2 =
∠6 =

Explanation:

Step1: Set up equations based on angle - relationship

Since line $a$ is parallel to line $b$, $\angle2$ and $\angle6$ are corresponding angles, so $m\angle2 = m\angle6$. Let $x=m\angle6$, then $m\angle2 = 5x - 68$.

Step2: Solve the equation

Set $5x-68=x$.
Subtract $x$ from both sides: $5x - x-68=x - x$, which simplifies to $4x-68 = 0$.
Add 68 to both sides: $4x-68 + 68=0 + 68$, getting $4x=68$.
Divide both sides by 4: $x=\frac{68}{4}=17$.

Step3: Find the measure of $\angle2$ and $\angle6$

Since $x = m\angle6$, then $m\angle6=17^{\circ}$.
And $m\angle2=m\angle6 = 17^{\circ}$.

Answer:

$\angle2 = 17^{\circ}$
$\angle6 = 17^{\circ}$