Question

the two triangles below are similar. also, m∠f=45° and m∠e=110° as shown below. find m∠j, m∠k, and m∠l. assume the triangles are accurately drawn.

Explanation:

Step1: Find angle G in triangle FEG

In triangle FEG, the sum of angles in a triangle is \(180^\circ\). So, \(m\angle G = 180^\circ - m\angle F - m\angle E\). Substituting the given values: \(m\angle G = 180^\circ - 45^\circ - 110^\circ = 25^\circ\).

Step2: Use similarity of triangles

Since triangles FEG and JKL are similar, corresponding angles are equal. So, \(m\angle J = m\angle G = 25^\circ\), \(m\angle K = m\angle E = 110^\circ\), and \(m\angle L = m\angle F = 45^\circ\).

Answer:

\(m\angle J = 25^\circ\), \(m\angle K = 110^\circ\), \(m\angle L = 45^\circ\)