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 = 76°
m∠3 = 104°
m∠4 =
▲ an error has occurred. please enter a number.

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles, $\angle2$ and $\angle4$ are vertical angles.

Step2: Use the property of adjacent angles (linear - pair)

Adjacent angles (linear - pair) sum to $180^{\circ}$. Given $m\angle1 = 104^{\circ}$, and $\angle1$ and $\angle2$ form a linear - pair. So $m\angle1+m\angle2 = 180^{\circ}$. Then $m\angle2=180 - 104=76^{\circ}$.

Step3: Use the vertical - angle property for $\angle4$

Since $\angle2$ and $\angle4$ are vertical angles (by the definition of vertical angles, two non - adjacent angles formed by the intersection of two lines). And we know that vertical angles are congruent. So $m\angle4=m\angle2$.

Answer:

$76$