Question

which pair of angles must be supplementary? ∠5 and ∠4 ∠1 and ∠6 ∠6 and ∠2 ∠2 and ∠5

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\).

Step2: Analyze each option

• Option \(\angle5\) and \(\angle4\):
• \(\angle5 = 90^{\circ}\), if \(\angle4\) is not \(90^{\circ}\) (from the figure, angles are formed by intersecting lines and right - angles are already marked as \(\angle2\) and \(\angle5\) is a right - angle). The sum of \(\angle4\) and \(\angle5\) is not \(180^{\circ}\).
• Option \(\angle1\) and \(\angle6\):
• These are adjacent angles but not forming a linear pair. Their sum is not \(180^{\circ}\).
• Option \(\angle6\) and \(\angle2\):
• \(\angle2 = 90^{\circ}\), \(\angle6\) is an acute angle. Their sum is not \(180^{\circ}\).
• Option \(\angle2\) and \(\angle5\):
• \(\angle2=90^{\circ}\), \(\angle5 = 90^{\circ}\). Then \(\angle2+\angle5=90^{\circ}+90^{\circ}=180^{\circ}\)

Answer:

\(\angle2\) and \(\angle5\)