Question

guided practice
midsegments of triangles
type your answer and then click or tap done.
what is ( m angle e f d )?
×60

Explanation:

Step1: Find the third angle of triangle \( \triangle DEY \)

The sum of angles in a triangle is \( 180^{\circ} \). In \( \triangle DEY \), if one angle is \( 45^{\circ} \) and another is \( 75^{\circ} \), then the third angle \( \angle DYE=180-(45 + 75)=60^{\circ} \).

Step2: Use the mid - segment property

Since \( ZY \) is a mid - segment (by the equal segment marks), \( \triangle DZY\sim\triangle DEF \) (by the mid - segment theorem which states that a line segment joining the mid - points of two sides of a triangle is parallel to the third side and half its length, and the triangles are similar). Corresponding angles of similar triangles are equal. So \( m\angle EFD=m\angle DZY \). Also, \( \angle DZY\) and \( \angle DYE\) are corresponding angles (because of the parallel lines and transversal properties from the mid - segment).

Answer:

\( 60^{\circ} \)