Question

the two triangles below are similar. also, ( mangle f = 15^circ ) and ( mangle e = 100^circ ) as shown below. find ( mangle r ), ( mangle s ), and ( mangle t ). assume the triangles are accurately drawn.

Explanation:

Step1: Find $\angle D$ (triangle sum)

$m\angle D = 180^\circ - 100^\circ - 15^\circ = 65^\circ$

Step2: Match similar triangle angles

By triangle similarity and accurate drawing:
$\angle R \cong \angle E$, $\angle S \cong \angle D$, $\angle T \cong \angle F$

Answer:

$m\angle R = 100^\circ$
$m\angle S = 65^\circ$
$m\angle T = 15^\circ$