Question

guided practice
midsegments of triangles
type your answer and then click or tap done.
what is ( m angle e f d )?

Explanation:

Step1: Use the property of mid - segment in a triangle

Since \(XY\) is a mid - segment of \(\triangle DEF\) (by the markings of equal segments), \(XY\parallel DF\).

Step2: Use the property of parallel lines and transversal

If \(XY\parallel DF\) and \(EF\) is a transversal, then \(\angle EYX=\angle EFD\) (corresponding angles).

Step3: Use the angle - sum property of a triangle

In \(\triangle DEY\), \(\angle D = 45^{\circ}\), \(\angle DEY=\angle D = 45^{\circ}\) (because \(DY = EY\) as per the markings). Then \(\angle DYE=180^{\circ}-45^{\circ}-45^{\circ}=90^{\circ}\).
In \(\triangle EYX\), \(\angle EYX = 180^{\circ}-75^{\circ}-45^{\circ}=60^{\circ}\)

Answer:

\(60^{\circ}\)