Question

current skill $ find the measure of angle 2. label optional

Explanation:

Step1: Identify vertical angles

Angle 5 = $6x + 169$, Angle 3 = $-9x -19$ (vertical angles are equal)

Step2: Set up equation

$6x + 169 = -9x -19$

Step3: Solve for x

$6x +9x = -19 -169$ → $15x = -188$ → $x = -12.533...$ (Wait, correction: Check angle 2 and 3 are supplementary? No, angle 2 and 3 are adjacent, angle 2 and 4 are vertical, angle 1 and 2... Wait, correct: The two red arrows mean the two lines are parallel, so corresponding angles angle 8 and angle 4 are equal. Angle 8 = $6x+169$, angle 4 = angle 2 (vertical). Angle 3 = $-9x-19$, angle 2 + angle3 = 180° (linear pair). Also angle 8 = angle 5 = $6x+169$ (vertical), angle 5 and angle 3 are same-side interior angles (parallel lines), so angle5 + angle3 =180°:
$6x+169 + (-9x-19) =180$
$-3x +150=180$
$-3x=30$
$x=-10$

Step4: Find angle3

angle3 = $-9(-10)-19=90-19=71°$

Step5: Find angle2

angle2 = 180° - angle3 =180-71=109°

Answer:

109°