To find the measure of the smaller angle when one angle is 3 less than twice its complement, we can follow these steps:
1. Let's denote the measure of the smaller angle as \( x \) degrees.
2. The complement of this angle would be \( 90 - x \) degrees, since the sum of an angle and its complement is 90 degrees.
3. According to the given information, the angle is 3 less than twice its complement. This can be written as an equation: \( x = 2(90 - x) - 3 \).
4. Now, we can solve this equation to find the value of \( x \).
5. Simplifying the equation: \( x = 180 - 2x - 3 \).
6. Combining like terms: \( x + 2x = 180 - 3 \).
7. Simplifying further: \( 3x = 177 \).
8. Dividing by 3 on both sides: \( x = 59 \).
9. Therefore, the measure of the smaller angle is 59 degrees.
