(c) problem 16: given $overline{ab}paralleloverline{jk}$, find y. after you enter your answer press go. y =
(c) problem 16: given $overline{ab}paralleloverline{jk}$, find y. after you enter your answer press go. y =
Answer
Answer:
$y = 27$
Explanation:
Step1: Use vertical - angle property
Since vertical angles are equal, the angle at the intersection of the lines is the same in both triangles. Also, because $\overline{AB}\parallel\overline{JK}$, the alternate - interior angles are equal. So, $2x - 9=y$ and $5x-21 + y=180$ (linear pair of angles).
Step2: Substitute $y = 2x - 9$ into the second equation
Substitute $y$ in $5x-21 + y=180$: [ \begin{align*} 5x-21+(2x - 9)&=180\ 5x-21 + 2x-9&=180\ 7x-30&=180 \end{align*} ]
Step3: Solve for $x$
Add 30 to both sides of the equation $7x - 30=180$: [ \begin{align*} 7x-30 + 30&=180+30\ 7x&=210 \end{align*} ] Divide both sides by 7: $x = 30$.
Step4: Solve for $y$
Substitute $x = 30$ into $y = 2x - 9$: [ \begin{align*} y&=2\times30-9\ y&=60 - 9\ y&=27 \end{align*} ]