Question

find the values of the variables for the parallelogram. m∠1 = 5y - 5 x = □, y = □, z = □ (type integers or decimals.)

Explanation:

Step1: Find x (alternate interior angles)

In a parallelogram, alternate interior angles are equal. So $x = 15$.

Step2: Find y (right angle property)

The diagonals of a rhombus (a type of parallelogram here) intersect at right angles, so $m\angle1 = 90^\circ$.
Set $5y - 5 = 90$:
$5y = 95$
$y = 19$

Step3: Find z (triangle angle sum)

The triangle with angles $z$, $15^\circ$, and $90^\circ$ sums to $180^\circ$:
$z + 15 + 90 = 180$
$z = 75$

Answer:

$x = 15$, $y = 19$, $z = 75$