Question

the figure shows three intersecting lines. lines g and h are perpendicular. how are ∠1 and ∠2 related? complete the equation. m∠1 + m∠2 = □°

Explanation:

Step1: Recall the definition of perpendicular lines

Perpendicular lines form a \(90^{\circ}\) angle.

Step2: Analyze the relationship between \(\angle1\), \(\angle2\) and the right - angle

Since lines \(g\) and \(h\) are perpendicular, the angle between them is \(90^{\circ}\). \(\angle1\), \(\angle2\) and the right - angle together form a straight line (\(180^{\circ}\)). But we know the right - angle part. Let's use the fact that the sum of angles around a point on a straight line. However, more simply, since the right - angle is \(90^{\circ}\) and \(\angle1+\angle2\) is part of the right - angle's adjacent angles. Wait, no, actually, looking at the figure, the three angles (\(90^{\circ}\), \(\angle1\), \(\angle2\)) are not. Wait, no, lines \(g\) and \(h\) are perpendicular (\(90^{\circ}\)). The sum of \(\angle1\) and \(\angle2\) is equal to \(90^{\circ}\) because the angle between \(g\) and \(h\) is \(90^{\circ}\) and there are no other angles in that particular right - angle split.

Answer:

\(90\)