Question

(c) problem 16: given $overline{ab}paralleloverline{jk}$, find y. after you enter your answer press go. y =

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 $y = 2x - 9$:
\[

$$\begin{align*} y&=2\times30-9\\ y&=60 - 9\\ y&=27 \end{align*}$$

\]

Answer:

$y = 27$