Question

the two triangles below are similar.
also, $m\angle e=30^{\circ}$ and $m\angle d=100^{\circ}$ as shown below.
find $m\angle w$, $m\angle x$, and $m\angle y$.
assume the triangles are accurately drawn.
$m\angle w = \square^{\circ}$
$m\angle x = \square^{\circ}$
$m\angle y = \square^{\circ}$

Explanation:

Step1: Find $\angle C$ in $\triangle EDC$

The sum of angles in a triangle is $180^\circ$.
$$m\angle C = 180^\circ - m\angle E - m\angle D = 180^\circ - 30^\circ - 100^\circ = 50^\circ$$

Step2: Match corresponding angles

For similar triangles, corresponding angles are congruent. From the diagram:
$\angle W \cong \angle C$, $\angle X \cong \angle E$, $\angle Y \cong \angle D$

Step3: Assign angle measures

$m\angle W = m\angle C = 50^\circ$
$m\angle X = m\angle E = 30^\circ$
$m\angle Y = m\angle D = 100^\circ$

Answer:

$m\angle W = 50^\circ$
$m\angle X = 30^\circ$
$m\angle Y = 100^\circ$