Question

find the measure of angle 6.

Explanation:

Step1: Identify supplementary angles

$\angle 6$ and $\angle 8$ are supplementary, so $m\angle 6 + m\angle 8 = 180^\circ$. Also, $\angle 8$ and $3x+169$ are corresponding angles, so $m\angle 8 = 3x+169$. Substitute: $m\angle 6 + (3x+169) = 180^\circ$, so $m\angle 6 = 11 - 3x$.

Step2: Set vertical angles equal

$\angle 6$ and $-4x-7$ are vertical angles, so $m\angle 6 = -4x -7$.

Step3: Solve for x

Set the two expressions for $m\angle 6$ equal:
$$11 - 3x = -4x -7$$
$$-3x +4x = -7 -11$$
$$x = -18$$

Step4: Calculate angle 6 measure

Substitute $x=-18$ into $m\angle 6 = -4x -7$:
$$m\angle 6 = -4(-18) -7 = 72 -7$$

Answer:

$65^\circ$