Question

1. if ∠1 and ∠2 are complementary angles, and m∠1 = 74°; find m∠2.
2. if ∠5 and ∠6 are complementary angles, and m∠6 = 6°; find m∠5.

) if ∠8 and ∠9 are complementary angles, and m∠9 = 11°; find m∠8.

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles add up to \(90^{\circ}\). So, if \(\angle1\) and \(\angle2\) are complementary, then \(m\angle1 + m\angle2=90^{\circ}\). Given \(m\angle1 = 74^{\circ}\), we can find \(m\angle2\) by subtracting \(m\angle1\) from \(90^{\circ}\).
\(m\angle2=90^{\circ}-m\angle1\)
\(m\angle2 = 90^{\circ}-74^{\circ}=16^{\circ}\)

Step2: Apply the same concept to \(\angle5\) and \(\angle6\)

Since \(\angle5\) and \(\angle6\) are complementary (\(m\angle5 + m\angle6=90^{\circ}\)), and \(m\angle6 = 6^{\circ}\)
\(m\angle5=90^{\circ}-m\angle6\)
\(m\angle5=90^{\circ}-6^{\circ}=84^{\circ}\)

Step3: Check for \(\angle8\) and \(\angle9\)

Wait, there is a mistake here. Complementary angles add up to \(90^{\circ}\), but \(m\angle9 = 11^{\circ}\). If we assume it's a typo and they are supplementary (add up to \(180^{\circ}\))
\(m\angle8=180^{\circ}-m\angle9\)
\(m\angle8=180^{\circ}-11^{\circ}=169^{\circ}\). But if we strictly follow complementary (which is \(90^{\circ}\)), \(90^{\circ}-11^{\circ}=79^{\circ}\), but \(11^{\circ}+79^{\circ}=90^{\circ}\)

Answer:

1. \(16^{\circ}\)
2. \(84^{\circ}\)
3. If complementary: \(79^{\circ}\), if supplementary: \(169^{\circ}\) (assuming the problem had a mis - label between complementary and supplementary for \(\angle8\) and \(\angle9\))