Question

current skill $\\$$
find the measure of angle 3.
(there is a diagram with intersecting lines, angles labeled 1, 3, 4, 6, 7, 8, and angle expressions: $4x + 163$, $5x + 188$)

Explanation:

Step1: Identify vertical angles

Vertical angles are equal, so $5x + 188 = 4x + 163$.

Step2: Solve for x

Subtract $4x$ from both sides: $x + 188 = 163$. Subtract 188: $x = -25$.

Step3: Find angle 1

Angle 1 = $4x + 163 = 4(-25) + 163 = -100 + 163 = 63^\circ$.

Step4: Find angle 3

Angle 1 and angle 3 are supplementary: $angle3 = 180^\circ - 63^\circ = 117^\circ$.

Answer:

117°