Question

the two triangles below are similar. also, ( mangle j = 45^circ ) and ( mangle l = 110^circ ) as shown below. find ( mangle e ), ( mangle f ), and ( mangle g ). assume the triangles are accurately drawn.

Explanation:

Step1: Find $\angle K$ in $\triangle KLJ$

The sum of angles in a triangle is $180^\circ$.
$m\angle K = 180^\circ - m\angle L - m\angle J = 180^\circ - 110^\circ - 45^\circ = 25^\circ$

Step2: Match corresponding angles (similar triangles)

By the triangle shape and similarity:
$\angle E$ corresponds to $\angle L$, $\angle F$ corresponds to $\angle J$, $\angle G$ corresponds to $\angle K$.
$m\angle E = m\angle L = 110^\circ$
$m\angle F = m\angle J = 45^\circ$
$m\angle G = m\angle K = 25^\circ$

Answer:

$m\angle E = 110^\circ$
$m\angle F = 45^\circ$
$m\angle G = 25^\circ$