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`