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 shows two intersecting lines, with angle 2 adjacent to 104° and angles 1,2,3,4 labeled around the intersection)

Explanation:

Step1: Find m∠2 (linear pair with ∠1)

$m\angle2 = 180^\circ - 104^\circ = 76^\circ$

Step2: Find m∠3 (vertical to ∠1)

$m\angle3 = m\angle1 = 104^\circ$

Step3: Find m∠4 (vertical to ∠2)

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

Answer:

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