The measure of angle E in the secant intersection is 21 degrees.
How to find the angle of intersected secant?
When two secants intersect outside a circle, the circle divides the secants into segments that are proportional with each other
Therefore,
m∠E = 1 / 2 (∠AB - ∠CD)
m∠E = 1 / 2 (80 - 38)
m∠E = 1 / 2 (42)
m∠E = 42 / 2
m∠E = 21 degrees.
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