Question

problem 21: find x and y.

Explanation:

Step1: Use vertical - angle property

$x=x - 67+67$, and vertical angles are equal. So $x=(x - 67)+67$. Also, $x$ and $x - 67$ are related to vertical - angle pairs. Since vertical angles are equal, we have $x+(x - 67)=180$ (linear - pair of angles). Solving $x+(x - 67)=180$ gives:
$2x-67 = 180$
$2x=180 + 67$
$2x=247$
$x = 134$

Step2: Use vertical - angle property for $y$

We know that the angle $y$ and $5y + 7$ are related. Since they are vertical angles, $y+(5y + 7)=180$ (linear - pair of angles).
$6y+7 = 180$
$6y=180 - 7$
$6y=173$
$y=\frac{173}{6}\approx14.6$

Answer:

$x = 134$, $y = 14.6$