Question

in the figure below, m∠3 = 109°. find m∠1, m∠2, and m∠4.

m∠1 = ☐°
m∠2 = ☐°
m∠4 = ☐°

Explanation:

Step1: Find \( m\angle1 \) (Vertical Angles)

Vertical angles are equal. \( \angle1 \) and \( \angle3 \) are vertical angles, so \( m\angle1 = m\angle3 \).
\( m\angle1 = 109^\circ \)

Step2: Find \( m\angle2 \) (Linear Pair)

\( \angle1 \) and \( \angle2 \) form a linear pair, so their measures add up to \( 180^\circ \). Let \( m\angle2 = x \), then \( 109^\circ + x = 180^\circ \). Solving for \( x \), we get \( x = 180^\circ - 109^\circ = 71^\circ \). So \( m\angle2 = 71^\circ \).

Step3: Find \( m\angle4 \) (Vertical Angles)

\( \angle2 \) and \( \angle4 \) are vertical angles, so \( m\angle4 = m\angle2 \).
\( m\angle4 = 71^\circ \)

Answer:

\( m\angle1 = 109^\circ \)
\( m\angle2 = 71^\circ \)
\( m\angle4 = 71^\circ \)