Question

two triangles below are similar.
find ( mangle w ), ( mangle x ), and ( mangle y ).
assume the triangles are accurately drawn.
(there is a triangle ( dec ) with ( angle d = 35^circ ), ( angle e = 90^circ ), and another triangle ( wxy ) shown. also, there are input boxes for ( mangle w ), ( mangle x ), ( mangle y ) with degree symbols.)

Explanation:

Step1: Identify corresponding angles

In triangle $CDE$, $\angle D = 35^\circ$, $\angle E = 90^\circ$. For similar triangles, corresponding angles are equal. $\angle W$ corresponds to $\angle E$, $\angle X$ corresponds to $\angle D$, $\angle Y$ corresponds to $\angle C$.

Step2: Calculate $\angle C$

Sum of angles in a triangle is $180^\circ$. $\angle C = 180^\circ - 90^\circ - 35^\circ = 55^\circ$.

Step3: Assign values

$m\angle W = m\angle E = 90^\circ$, $m\angle X = m\angle D = 35^\circ$, $m\angle Y = m\angle C = 55^\circ$.

Answer:

$m\angle W = 90^\circ$, $m\angle X = 35^\circ$, $m\angle Y = 55^\circ$