Question

in the figure below, m∠3 = 131°. find m∠1, m∠2, and m∠4. m∠1 = ☐° m∠2 = ☐° m∠4 = ☐°

Explanation:

Step1: Find \( m\angle1 \)

Vertical angles are equal. \( \angle1 \) and \( \angle3 \) are vertical angles, so \( m\angle1 = m\angle3 \).
\( m\angle1 = 131^\circ \)

Step2: Find \( m\angle2 \)

Linear pair angles are supplementary (sum to \( 180^\circ \)). \( \angle2 \) and \( \angle3 \) form a linear pair, so \( m\angle2 + m\angle3 = 180^\circ \).
\( m\angle2 = 180^\circ - 131^\circ = 49^\circ \)

Step3: Find \( m\angle4 \)

Vertical angles are equal. \( \angle4 \) and \( \angle2 \) are vertical angles, so \( m\angle4 = m\angle2 \).
\( m\angle4 = 49^\circ \)

Answer:

\( m\angle1 = 131^\circ \), \( m\angle2 = 49^\circ \), \( m\angle4 = 49^\circ \)