Question

PLZ HELP ME ASAP!!!!!

Answer 1

$TRUE:\\\\A.\ \overleftrightarrow{PR}\ and\ \overleftrightarrow{SQ}\ intersect\ at\ T\\\\C.\ \overline{ST}\ and\ \overline{QT}\ are\ both\ line\ segments\\\\FALSE:\\\\B.\ \overrightarrow{PT}\ and\ \overrightarrow{TR}\ are\ opposite\ rays,\ because\\\text{A pair of opposite rays are two rays that have}\\\text{the same endpoint and extend in opposite directions.}\ \\\\D.\ T\ is\ the\ midpoint\ of\ \overline{SQ},\\because \overleftrightarrow{PR}\ and\ \overleftrightarrow{SQ}\ can\ intersect\ at\ any\ point\ T.$

$3x+23\ and\ 4x+10\ are\ supplementary\ angles (\text{their sum is}\ 180^o).\\\\Therefore\ we\ have\ the\ equation:\\\\(3x+23)+(4x+10)=180\\\\(3x+4x)+(23+10)=180\\\\7x+33=180\qquad\text{subtract 33 from both sides}\\\\7x=147\qquad\text{divide both sides by 7}\\\\x=21\\\\4x+10=4(21)+10=84+10=94\\\\4x+10\ and\ y\ are\ vertical\ angles\ (\text{have the same measure}).\\\\Therefore\ y=94\\\\7x+33/y=7(21)+\dfrac{33}{94}=147+\dfrac{33}{94}=147\dfrac{33}{94}$