Question

find the value of $x$, $y$, and $z$ in the parallelogram below.
$73^\circ$
$(8x+2)^\circ$
$(6y-5)^\circ$
$(z-6)^\circ$
answer attempt 1 out of 2
$x = \square$ $y = \square$ $z = \square$

Explanation:

Step1: Use opposite angles property

In a parallelogram, opposite angles are equal. So $73 = x - 6$.
Solve for $x$: $x = 73 + 6 = 79$

Step2: Use consecutive angles property

Consecutive angles in a parallelogram are supplementary (sum to $180^\circ$). So $73 + (8z + 2) = 180$.
Simplify: $8z + 75 = 180$
$8z = 180 - 75 = 105$
$z = \frac{105}{8} = 13.125$

Step3: Use opposite angles property again

Opposite angles are equal, so $8z + 2 = 6y - 5$.
Substitute $z=13.125$: $8(13.125) + 2 = 6y - 5$
Calculate left side: $105 + 2 = 107$
Solve for $y$: $107 + 5 = 6y$
$112 = 6y$
$y = \frac{112}{6} = \frac{56}{3} \approx 18.67$

Answer:

$x = 79$, $y = \frac{56}{3}$, $z = \frac{105}{8}$