Question

the two triangles below are similar. also, ( mangle e = 50^circ ) and ( mangle f = 105^circ ) as shown below. find ( mangle j ), ( mangle k ), and ( mangle l ). assume the triangles are accurately drawn.

Explanation:

Step1: Find $\angle G$

The sum of angles in a triangle is $180^\circ$.
$$m\angle G = 180^\circ - m\angle E - m\angle F = 180^\circ - 50^\circ - 105^\circ = 25^\circ$$

Step2: Match similar triangle angles

Similar triangles have congruent corresponding angles. From the drawing: $\angle J \cong \angle G$, $\angle K \cong \angle F$, $\angle L \cong \angle E$.
$m\angle J = 25^\circ$, $m\angle K = 105^\circ$, $m\angle L = 50^\circ$

Answer:

$m\angle J = 25^\circ$, $m\angle K = 105^\circ$, $m\angle L = 50^\circ$