Question

what is m∠1?
m∠1 = 45 °
what are the remaining angle measures?
m∠2 = °
m∠3 = ? °
m∠4 = ? °

Explanation:

Step1: Find \( m\angle2 \)

Angles on a straight line sum to \( 180^\circ \). The angle adjacent to \( \angle2 \) is \( 45^\circ \), so \( m\angle2 = 180^\circ - 45^\circ = 135^\circ \).

Step2: Find \( m\angle3 \)

\( \angle3 \) and the \( 45^\circ \) angle are vertical angles (or alternate interior angles due to parallel lines). Vertical angles are equal, so \( m\angle3 = 45^\circ \).

Step3: Find \( m\angle4 \)

\( \angle4 \) and \( \angle2 \) are vertical angles (or \( \angle4 \) is supplementary to \( \angle3 \)). Since \( \angle2 = 135^\circ \), \( m\angle4 = 135^\circ \) (or \( 180^\circ - 45^\circ = 135^\circ \)).

Answer:

$m\angle2 = 135^\circ$, $m\angle3 = 45^\circ$, $m\angle4 = 135^\circ$