Let's denote the measure of the angle as $x$. The complement of an angle is given by $90^\circ - x$. According to the problem, the angle is 40 degrees less than its complement. Therefore, we can write the equation:

$x = (90^\circ - x) - 40^\circ$

Now, let's solve this equation:

$x = 90^\circ - x - 40^\circ$

Simplify the equation:

$x = 50^\circ - x$

Next, add $x$ to both sides to get:

$2x = 50^\circ$

Finally, divide both sides by 2:

$x = 25^\circ$

So, the measure of the angle is $25^\circ$.

Would you like more details or have any questions?

Here are five related questions:

1. What is the definition of complementary angles?
2. How do you find the supplement of an angle?
3. How do you solve for an angle if it is 20 degrees less than its complement?
4. What is the difference between complementary and supplementary angles?
5. What happens when an angle is equal to its complement?

Tip: Remember that complementary angles always add up to $90^\circ$.