Question

in the figure below, m∠1 = 32°. find m∠2, m∠3, and m∠4.

m∠2 = ☐°

m∠3 = ☐°

m∠4 = ☐°

Explanation:

Step1: Find \( m\angle2 \) (supplementary angles)

\( \angle1 \) and \( \angle2 \) are supplementary, so \( m\angle1 + m\angle2 = 180^\circ \).
Given \( m\angle1 = 32^\circ \), then \( m\angle2 = 180^\circ - 32^\circ = 148^\circ \).

Step2: Find \( m\angle3 \) (vertical angles)

\( \angle1 \) and \( \angle3 \) are vertical angles, so \( m\angle3 = m\angle1 = 32^\circ \).

Step3: Find \( m\angle4 \) (vertical angles)

\( \angle2 \) and \( \angle4 \) are vertical angles, so \( m\angle4 = m\angle2 = 148^\circ \).

Answer:

\( m\angle2 = \boldsymbol{148}^\circ \)
\( m\angle3 = \boldsymbol{32}^\circ \)
\( m\angle4 = \boldsymbol{148}^\circ \)