Question

the figure shows two parallel lines intersected by a transversal.
(1) what is ( mangle 1 )?
( mangle 1 = 45^circ )
(2) what are the remaining angle measures?
( mangle 2 = ? )
( mangle 3 = ? )
( mangle 4 = ? )

Explanation:

Step1: Identify ∠2's measure

∠2 and the given 45° angle are corresponding angles (parallel lines cut by transversal), so they are congruent.
$m\angle 2 = 45^\circ$

Step2: Identify ∠3's measure

∠3 and the given 135° angle are corresponding angles, so they are congruent.
$m\angle 3 = 135^\circ$

Step3: Identify ∠4's measure

∠4 and the given 45° angle are vertical angles, so they are congruent.
$m\angle 4 = 45^\circ$

Answer:

$m\angle 2 = 45^\circ$
$m\angle 3 = 135^\circ$
$m\angle 4 = 45^\circ$