Question

c) 1) if ∠2 and ∠3 are supplementary angles, and m∠3 = 17°; find m∠2.

1. if ∠5 and ∠6 are supplementary angles, and m∠5 = 124°; find m∠6.
2. if ∠8 and ∠9 are supplementary angles, and m∠9 = 86°; find m∠8.

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles add up to \(180^{\circ}\). So, if \(\angle A\) and \(\angle B\) are supplementary, then \(m\angle A + m\angle B=180^{\circ}\).

Step2: Solve for \(m\angle2\)

Given \(m\angle3 = 17^{\circ}\) and \(\angle2\) and \(\angle3\) are supplementary.
Using the formula \(m\angle2+m\angle3 = 180^{\circ}\), we substitute \(m\angle3\):
\(m\angle2=180^{\circ}-m\angle3\)
\(m\angle2 = 180^{\circ}- 17^{\circ}=163^{\circ}\)

Step3: Solve for \(m\angle6\)

Given \(m\angle5 = 124^{\circ}\) and \(\angle5\) and \(\angle6\) are supplementary.
Using the formula \(m\angle5+m\angle6 = 180^{\circ}\), we substitute \(m\angle5\):
\(m\angle6=180^{\circ}-m\angle5\)
\(m\angle6=180^{\circ}-124^{\circ} = 56^{\circ}\)

Step4: Solve for \(m\angle8\)

Given \(m\angle9 = 86^{\circ}\) and \(\angle8\) and \(\angle9\) are supplementary.
Using the formula \(m\angle8+m\angle9 = 180^{\circ}\), we substitute \(m\angle9\):
\(m\angle8=180^{\circ}-m\angle9\)
\(m\angle8=180^{\circ}-86^{\circ}=94^{\circ}\)

Answer:

1. \(m\angle2 = 163^{\circ}\)
2. \(m\angle6 = 56^{\circ}\)
3. \(m\angle8 = 94^{\circ}\)