Question

Solve for "X" and "Y"

Answer 1

`2(3x+4)^o\ and\ (9x-10)^o\ are\ vertical\ angles.\\\\\text{The measures of a vertical angles are equal}\\\\Therefore\ we\ have\ the\ equation:\\\\2(3x+4)=9x-10\qquad|\text{use distributive property}\\\\(2)(3x)+(2)(4)=9x-10\\\\6x+8=9x-10\qquad|-8\\\\6x=9x-18\qquad|-9x\\\\-3x=-18\qquad|:(-3)\\\\\boxed{x=6}`

`2(4y+4)^o\ and\ (7y+24)^o\ are\ vertical\ angles.\\\\Therefore\ we\ have\ the\ equation:\\\\2(4y+4)=7y+24\qquad|\text{use distributive property}\\\\(2)(4y)+(2)(4)=7y+24\\\\8y+8=7y+24\qquad|-8\\\\8y=7y+16\qquad|-7y\\\\\boxed{y=16}`