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Two parallel lines are intersected by a transversal. If one angle is 75 degrees, find the value of y.

Mathematics

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Here are the solutions to the geometry problems.

: Parallel lines and a transversal

The image shows two parallel lines intersected by a transversal. We need to find the value of yy.
The angle given is 75∘75^\circ. Let's call the intersection points M (on line AB) and K (on line CD).
The angle ∠EMB=75∘\angle EMB = 75^\circ.
The angle we need to find is y=∠DKEy = \angle DKE.

Step 1: Identify the relationship between the given angle and an angle related to yy.
The angle ∠EMB=75∘\angle EMB = 75^\circ.
The angle vertically opposite to ∠EMB\angle EMB is ∠AMF\angle AMF.
Therefore, $\angle AMF = 75^\

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