Question

the two triangles below are similar. also, m∠r = 15° and m∠t = 105° as shown below. find m∠d, m∠e, and m∠f. assume the triangles are accurately drawn.

Explanation:

Step1: Recall angle - property of similar triangles

Corresponding angles of similar triangles are equal.

Step2: Identify corresponding angles

Assume $\angle R$ corresponds to $\angle D$, $\angle T$ corresponds to $\angle E$, and $\angle S$ corresponds to $\angle F$.

Step3: Find $\angle D$

Since $\angle R = 15^{\circ}$ and $\angle D$ corresponds to $\angle R$, $m\angle D=15^{\circ}$.

Step4: Find $\angle E$

Since $\angle T = 105^{\circ}$ and $\angle E$ corresponds to $\angle T$, $m\angle E = 105^{\circ}$.

Step5: Find $\angle F$

The sum of angles in a triangle is $180^{\circ}$. For $\triangle DEF$, $m\angle F=180-(m\angle D + m\angle E)=180-(15 + 105)=60^{\circ}$.

Answer:

$m\angle D = 15^{\circ}$
$m\angle E = 105^{\circ}$
$m\angle F = 60^{\circ}$