Question

the two triangles below are similar. also, ( mangle x = 35^circ ) and ( mangle w = 85^circ ) as shown below. find ( mangle c ), ( mangle d ), and ( mangle e ). assume the triangles are accurately drawn.

Explanation:

Step1: Find $\angle Y$ in $\triangle WYX$

The sum of angles in a triangle is $180^\circ$.
$$m\angle Y = 180^\circ - m\angle W - m\angle X = 180^\circ - 85^\circ - 35^\circ = 60^\circ$$

Step2: Match corresponding angles

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

Step3: Assign angle measures

$m\angle C = m\angle W = 85^\circ$
$m\angle D = m\angle X = 35^\circ$
$m\angle E = m\angle Y = 60^\circ$

Answer:

$m\angle C = 85^\circ$
$m\angle D = 35^\circ$
$m\angle E = 60^\circ$