Question

use the diagram below to find x, y and z. 9. x = _ y = _ z = ___

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle with measure $72^{\circ}$ and the angle with measure $2x^{\circ}$ are vertical angles. So, $2x = 72$.
$2x=72$

Step2: Solve for $x$

Divide both sides of the equation $2x = 72$ by 2.
$x=\frac{72}{2}=36$

Step3: Use corresponding - angle property

The angle with measure $(5y + 2)^{\circ}$ and the $72^{\circ}$ angle are corresponding angles. So, $5y+2 = 72$.
$5y+2 = 72$

Step4: Solve for $y$

Subtract 2 from both sides: $5y=72 - 2=70$. Then divide both sides by 5. $y=\frac{70}{5}=14$

Step5: Use linear - pair property

The angle with measure $4z^{\circ}$ and the $72^{\circ}$ angle form a linear - pair. So, $4z+72 = 180$.
$4z+72 = 180$

Step6: Solve for $z$

Subtract 72 from both sides: $4z=180 - 72 = 108$. Then divide both sides by 4. $z=\frac{108}{4}=27$

Answer:

$x = 36$, $y = 14$, $z = 27$