Question

in the diagram, the measure of angle 3 is 89°, and the measure of angle 6 is 88°. what is the measure of angle 4? 88°

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles add up to \(180^{\circ}\). Angle \(3\) and angle \(4\) are supplementary.
So, \(\angle3+\angle4 = 180^{\circ}\)

Step2: Solve for \(\angle4\)

Given \(\angle3 = 89^{\circ}\), then \(\angle4=180^{\circ}-\angle3\)
Substitute \(\angle3 = 89^{\circ}\) into the formula: \(\angle4 = 180^{\circ}- 89^{\circ}=91^{\circ}\)

But wait, maybe there is a mistake. Let's check again. Wait, no, another approach: looking at the vertical - angle and parallel - line properties. Wait, no, the key is that \(\angle3\) and \(\angle4\) are adjacent angles forming a linear pair (supplementary).

Answer:

\(91^{\circ}\)