The statements A and D are true.
Based on the diagram, here are the true statements:
A. measure of angle EDF=53 degrees:
This is true because angle EDF and angle CDE are supplementary angles, meaning they add up to 180 degrees.
Since we're given that measure of angle CDE=127 degrees, we can find measure of angle EDF by subtracting 127 from 180:
measure of angle EDF = 180 degrees - 127 degrees = 53 degrees.
D. measure of angle GAE=53 degrees:
This is true because angle EDF and angle GAE are corresponding angles.
Corresponding angles are pairs of angles that are on opposite sides of a transversal and that share a common endpoint with the transversal.
They are equal in measure.
Since we've already determined that measure of angle EDF=53 degrees, we can conclude that measure of angle GAE=53 degrees as well.
Therefore, the statements A and D are true.