Question

find ( mangle u ) in parallelogram ( uvwx ).
( mangle u = square^circ )
submit

Explanation:

Step1: Use parallelogram consecutive angles property

Consecutive angles in a parallelogram are supplementary, so:
$$z + (z + 60^\circ) = 180^\circ$$

Step2: Simplify and solve for $z$

Combine like terms and isolate $z$:
$$2z + 60^\circ = 180^\circ$$
$$2z = 180^\circ - 60^\circ = 120^\circ$$
$$z = \frac{120^\circ}{2} = 60^\circ$$

Step3: Use parallelogram opposite angles property

$\angle U$ is opposite $\angle W$, so $m\angle U = z + 60^\circ$:
$$m\angle U = 60^\circ + 60^\circ = 120^\circ$$

Answer:

$120^\circ$