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 right - angle (\(90^{\circ}\)).

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

Since lines \(g\) and \(h\) are perpendicular, the angle between them is \(90^{\circ}\). Also, \(\angle1\), \(\angle2\) and the right - angle are related as \(m\angle1 + m\angle2+90^{\circ}=180^{\circ}\) (because they form a straight - line angle, and the measure of a straight - line angle is \(180^{\circ}\)).

Step3: Solve for \(m\angle1 + m\angle2\)

Subtract \(90^{\circ}\) from both sides of the equation \(m\angle1 + m\angle2+90^{\circ}=180^{\circ}\).

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Answer:

\(90\)