Question

name the two pairs of vertical angles in the figure.
∠1 and ∠3
∠2 and ∠4
m∠1 = 104°. find the remaining three angle measures.
m∠2 = □°
m∠3 =? °
m∠4 =? °

Explanation:

Step1: Find \( m\angle2 \)

\(\angle1\) and \(\angle2\) are supplementary (form a linear pair), so \( m\angle1 + m\angle2 = 180^\circ \). Given \( m\angle1 = 104^\circ \), then \( m\angle2 = 180^\circ - 104^\circ = 76^\circ \).

Step2: Find \( m\angle3 \)

\(\angle1\) and \(\angle3\) are vertical angles, so they are equal. Thus, \( m\angle3 = m\angle1 = 104^\circ \).

Step3: Find \( m\angle4 \)

\(\angle2\) and \(\angle4\) are vertical angles, so they are equal. Thus, \( m\angle4 = m\angle2 = 76^\circ \).

Answer:

\( m\angle2 = 76^\circ \)
\( m\angle3 = 104^\circ \)
\( m\angle4 = 76^\circ \)