Question

the two triangles below are similar. also, m∠c = 30° and m∠d = 100° as shown below. find m∠w, m∠x, and m∠y. assume the triangles are accurately drawn.

Explanation:

Step1: Recall property of similar triangles

Corresponding angles of similar triangles are equal. So $\angle W=\angle D$ and $\angle Y = \angle C$.

Step2: Find $m\angle W$

Since $\angle W=\angle D$ and $m\angle D = 100^{\circ}$, then $m\angle W=100^{\circ}$.

Step3: Find $m\angle Y$

Since $\angle Y=\angle C$ and $m\angle C = 30^{\circ}$, then $m\angle Y=30^{\circ}$.

Step4: Use angle - sum property of a triangle

The sum of interior angles of a triangle is $180^{\circ}$. For $\triangle WXY$, we have $m\angle W+m\angle X+m\angle Y=180^{\circ}$. Substitute $m\angle W = 100^{\circ}$ and $m\angle Y=30^{\circ}$ into the equation: $100^{\circ}+m\angle X + 30^{\circ}=180^{\circ}$. Then $m\angle X=180^{\circ}-(100^{\circ}+30^{\circ})=50^{\circ}$.

Answer:

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