Given ∠ BAE = ∠ DAC
=> the two angles are vertical angles
=> BAD and CAE are both straight lines.
Also given
12x-10 = ∠ BAE = ∠ DAC = 5x+53
=>
12x-10=5x-53
Solving for x gives
12x-5x=53+10
=> x=9
=> ∠ BAE = ∠ DAC = 9*12-10 = 98 °
Since BAD is a straight line,
∠ BAE and DAE are supplementary,
=>
BAE + DAE = 180 °
=> ∠ DAE=180-BAE=180-98=82 °
=>
Measure of arc ED = 82 °
