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 triangle angle - sum property

In \(\triangle DEY\), we know one angle is \(45^{\circ}\) and another is \(75^{\circ}\). The sum of angles in a triangle is \(180^{\circ}\). Let the third angle in \(\triangle DEY\) be \( \angle DYE\). So, \( \angle DYE=180-(45 + 75)\).

$$ \angle DYE=180 - 120=60^{\circ}$$

Step2: Use the mid - segment and parallel line properties

Since \(ZY\) and \(XY\) are mid - segments (by the markings of equal segments), \(ZY\parallel EF\) and \(XY\parallel DF\). Then, quadrilateral \(ZDFY\) is a parallelogram (a quadrilateral with both pairs of opposite sides parallel). In a parallelogram, opposite angles are equal. So, \(m\angle EFD=m\angle DYE\)

Answer:

\(60\)