Question

in the figure below, m∠1 = 78°. find m∠2, m∠3, and m∠4.
(figure of intersecting lines with angles 1,2,3,4 labeled)
m∠2 = □°
m∠3 = □°
m∠4 = □°

Explanation:

Step1: Find m∠2 (vertical to ∠1)

Vertical angles are equal, so \( m\angle2 = m\angle1 = 78^\circ \)

Step2: Find m∠3 (supplementary to ∠1)

Linear pair sum to \( 180^\circ \), so \( m\angle3 = 180^\circ - 78^\circ = 102^\circ \)

Step3: Find m∠4 (vertical to ∠3)

Vertical angles are equal, so \( m\angle4 = m\angle3 = 102^\circ \)

Answer:

\( m\angle2 = 78^\circ \)
\( m\angle3 = 102^\circ \)
\( m\angle4 = 102^\circ \)