Question

1. $\angle 2$ and $\angle 4$ and $\angle 4$ and $\angle 5$ are supplementary. $m\angle 4 = 105^{\circ}$.

Explanation:

Assuming we need to find \( m\angle2 \) and \( m\angle5 \) (since the problem mentions supplementary angles and gives \( m\angle4 = 105^\circ \)):

Step 1: Find \( m\angle5 \)

Supplementary angles sum to \( 180^\circ \). So \( m\angle4 + m\angle5 = 180^\circ \).
Substitute \( m\angle4 = 105^\circ \):
\( 105^\circ + m\angle5 = 180^\circ \)
\( m\angle5 = 180^\circ - 105^\circ = 75^\circ \)

Step 2: Find \( m\angle2 \)

Given \( \angle2 \) and \( \angle4 \) are supplementary, so \( m\angle2 + m\angle4 = 180^\circ \).
Substitute \( m\angle4 = 105^\circ \):
\( m\angle2 + 105^\circ = 180^\circ \)
\( m\angle2 = 180^\circ - 105^\circ = 75^\circ \)

Answer:

\( m\angle2 = 75^\circ \), \( m\angle5 = 75^\circ \)