Question

Help I don't get this question at all

Answer 1

A. $\angle7$ and $\angle8$ are congruent because they are opposite to one another across the intersection of lines C and D. (We call $\angle7$ and $\angle8$ a "vertical angle pair".)

B. For the same reason $\angle7$ and $\angle8$ are congruent, we know that the angles with measures $5y-29$ and $3y+19$ are also congruent. This means $5y-29=3y+19$, which we can solve for $y$.

C. $5y-29=3y+19\implies2y=48\implies y=24$

While vertical angle pairs are congruent, adjacent angle pairs are supplementary. This means that $5y-29$ and the measure of $\angle7$ (or $\angle8$) add to 180 degrees. Similarly, $3y+19$ and the measure of $\angle7$ (or $\angle8$) also add to 180 degrees.

With $y=24$, we find

$m\angle7+(5y-29)^\circ=180^\circ\implies m\angle7=180^\circ-(5(24)-29)^\circ$

$\implies m\angle7=m\angle8=89^\circ$