Question

in the figure below, m∠4 = 108° find m∠1, m∠2, and m∠3

Explanation:

Step1: Find \( m\angle1 \) (supplementary angles)

\( \angle1 \) and \( \angle4 \) are supplementary, so \( m\angle1 + m\angle4 = 180^\circ \). Given \( m\angle4 = 108^\circ \), then \( m\angle1 = 180^\circ - 108^\circ = 72^\circ \).

Step2: Find \( m\angle2 \) (vertical angles with \( \angle4 \))

\( \angle2 \) and \( \angle4 \) are vertical angles, so \( m\angle2 = m\angle4 = 108^\circ \).

Step3: Find \( m\angle3 \) (vertical angles with \( \angle1 \))

\( \angle3 \) and \( \angle1 \) are vertical angles, so \( m\angle3 = m\angle1 = 72^\circ \).

Answer:

\( m\angle1 = 72^\circ \), \( m\angle2 = 108^\circ \), \( m\angle3 = 72^\circ \)