Question

in the figure below, m ∠ 3 = 78°. find m ∠ 1, m ∠ 2, and m ∠ 4.

Explanation:

Step1: Identify Vertical Angles (∠1 and ∠3)

Vertical angles are equal, so \( m\angle1 = m\angle3 \).
\( m\angle1 = 78^\circ \)

Step2: Identify Supplementary Angles (∠2 and ∠3)

Angles on a straight line sum to \( 180^\circ \), so \( m\angle2 + m\angle3 = 180^\circ \).
\( m\angle2 = 180^\circ - 78^\circ = 102^\circ \)

Step3: Identify Vertical Angles (∠4 and ∠2)

Vertical angles are equal, so \( m\angle4 = m\angle2 \).
\( m\angle4 = 102^\circ \)

Answer:

\( m\angle1 = 78^\circ \)
\( m\angle2 = 102^\circ \)
\( m\angle4 = 102^\circ \)