Question

what is the sum of the measures of angles 6, 3, and 4?
line g || line h
image not drawn to scale

Explanation:

Step1: Find the measure of angle 6

Since angle 6 and the \(53^{\circ}\) angle are vertical angles, they are equal. So, \(\angle6 = 53^{\circ}\).

Step2: Find the measure of angle 3

Because line \(g\parallel\) line \(h\), and the transversal cuts them. Angle 3 and the \(53^{\circ}\) angle are alternate - interior angles. So, \(\angle3=53^{\circ}\).

Step3: Find the measure of angle 4

Angle 4 and angle 3 are supplementary (they form a linear pair). So, \(\angle4 = 180^{\circ}-\angle3\). Substituting \(\angle3 = 53^{\circ}\), we get \(\angle4=180 - 53=127^{\circ}\).

Step4: Calculate the sum of angles 6, 3, and 4

\(\angle6+\angle3+\angle4=53 + 53+127\)

$$
LATEXBLOCK0
$$

Answer:

\(233^{\circ}\)