Question

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

Explanation:

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

The sum of angles in a triangle is \( 180^{\circ} \). Given one angle is \( 45^{\circ} \) and assume the triangle \( \triangle DEY \) has two equal sides (marked with one tick), so it is an isosceles triangle. But wait, actually, we can use the angle - sum property. Let's re - think. Wait, no, we should use the fact that the sum of angles in a triangle is \( 180^{\circ} \).
Another approach: The triangle \( \triangle EXY \): we know that the sum of angles in a triangle is \( 180^{\circ} \). If we assume that the triangle has angles where one is \( 45^{\circ} \) (from \( \triangle D... \) part, but actually, no, wait, the correct way is:
The sum of angles in \( \triangle EXY \) is \( 180^{\circ} \). We know two angles (wait, no, actually, we can use the property that in a triangle, \( \angle EXY=180^{\circ}-45^{\circ}-75^{\circ}\)

Step2: Calculate \( m\angle EXY \)

Using the formula \( \angle EXY = 180^{\circ}-\alpha-\beta\), where \( \alpha = 45^{\circ}\) and \( \beta=75^{\circ}\)

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Answer:

\(60^{\circ}\)