If the rectangle has a fixed width of 300, it means that

where
and
are width and length, respetively.
So given the length
, the are would be

Based on the central angle theorem, the measure of angle AEB is: 140°.
<h3>What is the Central Angle Theorem?</h3>
According to the central angle theorem, the measure of an intercepted arc = measure of the central angle.
Arc AB = 140° [intercepted arc]
Angle AEB is the central angle.
Thus, based on the central angle theorem, the measure of angle AEB is: 140°.
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<h3>
Answer: 73</h3>
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Work Shown:
Check out the diagram below. Note the pair of alternate interior angles that are congruent (each 37 degrees). Then focus on triangle ABC. With the reference angle being at A, this means we use the tangent function because BC = x is the opposite side and AB = 97 is the adjacent side.
tan(angle) = opposite/adjacent
tan(A) = BC/AB
tan(37) = x/97
97*tan(37) = x
x = 97*tan(37)
x = 73.094742859971
For the last step, you'll need a calculator that can handle trig functions. Make sure the calculator is in degree mode. The result here is approximate. This rounds to 73 when rounding to the nearest whole number.