Question

exit ticket directions: use the vertical angles to find the angles x, y, and z. x=_ y=25° z=_

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal.

Step2: Find the value of x

Since x and the 75 - degree angle are vertical angles, $x = 75^{\circ}$.

Step3: Find the value of z

The sum of angles around a point is 360 degrees. We know $y = 25^{\circ}$ and $x = 75^{\circ}$. Also, the angle opposite to y is 25 degrees and the angle opposite to x is 75 degrees. So, $z=360-(2\times75 + 2\times25)=360-(150 + 50)=160^{\circ}$.

Answer:

$x = 75^{\circ}$
$y = 25^{\circ}$
$z = 160^{\circ}$