Question

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Explanation:

Step1: Find \( m\angle1 \)

\( \angle1 \) and \( \angle3 \) are corresponding angles (parallel lines cut by transversal), so \( m\angle1 = m\angle3 = 58^\circ \).

Step2: Find \( m\angle2 \)

\( \angle2 \) and \( \angle3 \) are supplementary (linear pair), so \( m\angle2 = 180^\circ - 58^\circ = 122^\circ \).

Step3: Find \( m\angle4 \)

\( \angle4 \) and \( \angle3 \) are supplementary (linear pair), so \( m\angle4 = 180^\circ - 58^\circ = 122^\circ \).

Step4: Find \( m\angle5 \)

\( \angle5 \) and \( \angle3 \) are vertical angles, so \( m\angle5 = m\angle3 = 58^\circ \).

Step5: Find \( m\angle6 \)

\( \angle6 \) and \( \angle3 \) are supplementary (linear pair), so \( m\angle6 = 180^\circ - 58^\circ = 122^\circ \).

Step6: Find \( m\angle7 \)

\( \angle7 \) and \( \angle3 \) are corresponding angles, so \( m\angle7 = m\angle3 = 58^\circ \).

Step7: Find \( m\angle8 \)

\( \angle8 \) and \( \angle3 \) are supplementary (linear pair), so \( m\angle8 = 180^\circ - 58^\circ = 122^\circ \).

Answer:

\( m\angle1 = 58^\circ \)
\( m\angle2 = 122^\circ \)
\( m\angle3 = 58^\circ \)
\( m\angle4 = 122^\circ \)
\( m\angle5 = 58^\circ \)
\( m\angle6 = 122^\circ \)
\( m\angle7 = 58^\circ \)
\( m\angle8 = 122^\circ \)