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To determine the measure of angle E, it's essential to first understand the relationship between complementary angles. Complementary angles are two angles whose measures add up to 90 degrees.

In this scenario, angle E is described as being 40 degrees smaller than its complement. If we denote the measure of angle E as \(x\), then its complementary angle would be \(90 - x\). According to the problem, angle E is 40 degrees smaller than its complement, which can be expressed mathematically as:

\[ x = (90 - x) - 40 \]

By simplifying this equation, we first isolate \(x\):

\[ x = 90 - x - 40 \]

\[ x + x = 90 - 40 \]

\[ 2x = 50 \]

\[ x = 25 \]

Thus, angle E measures 25 degrees. This confirms that the correct answer aligns with the relationship defined in the question. The logic demonstrates the nature of complementary angles along with basic algebra to find the measure of angle E, validating the answer as 25 degrees. Angle measures of 45 degrees, 60 degrees, and 90 degrees do not satisfy the criteria of being 40 degrees smaller than their complementary angles.