Question

name the two pairs of vertical angles in the figure.
∠1 and ∠3
∠2 and ∠4
m∠1 = 104°. find the remaining three angle measures.
m∠2 =

m∠3 =?
m∠4 =?
(figure: two intersecting lines forming angles 1,2,3,4 with 104° marked between angle 1 and angle 2)

Explanation:

Step1: Find $m\angle2$ (supplementary to $\angle1$)

Angles on a straight line sum to $180^\circ$.
$m\angle2 = 180^\circ - m\angle1 = 180^\circ - 104^\circ = 76^\circ$

Step2: Find $m\angle3$ (vertical to $\angle1$)

Vertical angles are congruent.
$m\angle3 = m\angle1 = 104^\circ$

Step3: Find $m\angle4$ (vertical to $\angle2$)

Vertical angles are congruent.
$m\angle4 = m\angle2 = 76^\circ$

Answer:

$m\angle2 = 76^\circ$
$m\angle3 = 104^\circ$
$m\angle4 = 76^\circ$