Question

in the figure below, m∠2 = 46°. find m∠1, m∠3, and m∠4. m∠1 = \\(\square\\)° m∠3 = \\(\square\\)° m∠4 = \\(\square\\)°

Explanation:

Step1: Find \( m\angle1 \)

\(\angle1\) and \(\angle2\) are supplementary (form a linear pair), so \( m\angle1 + m\angle2 = 180^\circ \). Given \( m\angle2 = 46^\circ \), then \( m\angle1 = 180^\circ - 46^\circ = 134^\circ \).

Step2: Find \( m\angle3 \)

\(\angle3\) and \(\angle2\) are supplementary (form a linear pair), so \( m\angle3 + m\angle2 = 180^\circ \). Thus, \( m\angle3 = 180^\circ - 46^\circ = 134^\circ \).

Step3: Find \( m\angle4 \)

\(\angle4\) and \(\angle2\) are vertical angles, so they are equal. Thus, \( m\angle4 = m\angle2 = 46^\circ \).

Answer:

\( m\angle1 = 134^\circ \), \( m\angle3 = 134^\circ \), \( m\angle4 = 46^\circ \)