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:

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