Answer:
y = 3/2x by making use of angle relationships in triangles
Step-by-step explanation:
Here's one way to solve it.
∠ADE is an external angle to ΔBDE. As such, its measure will be the sum of the measures of the remote interior angles, ∠DBE and ∠DEB:
∠ADE = 2x° +y°
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If we call the intersection point of AC and DE point G, then ∠AGE is an exterior angle to ΔADG. As such, its measure is the sum of the remote interior angles:
∠AGE = ∠GAD +∠GDA
3y° = x° +(2x° +y°)
2y = 3x . . . . . . . . . . subtract y°, collect terms, divide by °
y = (3/2)x . . . . . . . . divide by 2
