Question

3x + 169, -4x - 7, find the measure of angle 6

Explanation:

Step1: Identify supplementary angle pair

Angle 4 ($3x+169$) and angle 6 ($-4x-7$) are same-side interior angles, so they are supplementary:
$$(3x + 169) + (-4x - 7) = 180$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$:
$$-x + 162 = 180$$
$$-x = 180 - 162$$
$$-x = 18$$
$$x = -18$$

Step3: Substitute $x$ to find angle 6

Plug $x=-18$ into the expression for angle 6:
$$-4(-18) - 7 = 72 - 7$$

Answer:

$65$