Question

in the figure shown, m || n. if m∠1=(5x + 8)° and m∠8 = 122°, determine the measures of the other seven angles in the figure.

Explanation:

Answer:

Since \(m\parallel n\), \(\angle1\) and \(\angle8\) are alternate - exterior angles. So \(5x + 8=122\), solving for \(x\) gives \(x = 22.8\).
\(m\angle1=(5\times22.8 + 8)^{\circ}=122^{\circ}\)
\(m\angle2 = 180 - 122=58^{\circ}\)
\(m\angle3 = 122^{\circ}\)
\(m\angle4 = 58^{\circ}\)
\(m\angle5 = 58^{\circ}\)
\(m\angle6 = 122^{\circ}\)
\(m\angle7 = 58^{\circ}\)