Question

14 of 16
in the picture, line a is parallel to line b.
m∠2 is 68 less than 5 times m∠6.
∠2=
∠6=

Explanation:

Step1: Identify 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: Set up the equation

Because $m\angle2=m\angle6$, we have the equation $x = 5x-68$.

Step3: Solve the equation

Subtract $x$ from both sides: $0 = 5x - x-68$, which simplifies to $4x=68$. Then divide both sides by 4: $x=\frac{68}{4}=17$.

Step4: Find the measure of the angles

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

Answer:

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