A. [tex]\angle7[/tex] and [tex]\angle8[/tex] are congruent because they are opposite to one another across the intersection of lines C and D. (We call [tex]\angle7[/tex] and [tex]\angle8[/tex] a "vertical angle pair".)
B. For the same reason [tex]\angle7[/tex] and [tex]\angle8[/tex] are congruent, we know that the angles with measures [tex]5y-29[/tex] and [tex]3y+19[/tex] are also congruent. This means [tex]5y-29=3y+19[/tex], which we can solve for [tex]y[/tex].
C. [tex]5y-29=3y+19\implies2y=48\implies y=24[/tex]
While vertical angle pairs are congruent, adjacent angle pairs are supplementary. This means that [tex]5y-29[/tex] and the measure of [tex]\angle7[/tex] (or [tex]\angle8[/tex]) add to 180 degrees. Similarly, [tex]3y+19[/tex] and the measure of [tex]\angle7[/tex] (or [tex]\angle8[/tex]) also add to 180 degrees.
With [tex]y=24[/tex], we find
[tex]m\angle7+(5y-29)^\circ=180^\circ\implies m\angle7=180^\circ-(5(24)-29)^\circ[/tex]
[tex]\implies m\angle7=m\angle8=89^\circ[/tex]
