Question

the two triangles below are similar. also, ( mangle f = 60^{circ} ) and ( mangle e = 95^{circ} ) as shown below. find ( mangle j ), ( mangle k ), and ( mangle l ). assume the triangles are accurately drawn.

Explanation:

Step1: Use the property of similar triangles

Similar triangles have equal corresponding angles. So, \(m\angle J=m\angle G\), \(m\angle K = m\angle E\), \(m\angle L=m\angle F\).

Step2: Calculate \(m\angle G\)

In \(\triangle EFG\), using the angle - sum property of a triangle (\(m\angle E+m\angle F + m\angle G=180^{\circ}\)).
Substitute \(m\angle E = 95^{\circ}\) and \(m\angle F=60^{\circ}\) into the formula:
\(95^{\circ}+60^{\circ}+m\angle G=180^{\circ}\)
\(m\angle G=180^{\circ}-(95^{\circ} + 60^{\circ})\)
\(m\angle G=180^{\circ}-155^{\circ}\)
\(m\angle G = 25^{\circ}\)

Answer:

\(m\angle J = 25^{\circ}\), \(m\angle K=95^{\circ}\), \(m\angle L = 60^{\circ}\)