The angle in question measures 13 degrees, which is found by establishing the angle as x degrees, setting up an equation according to the problem statement, and solving for x to find the answer.
To find the measure of an angle that is 141 degrees less than twice its complement, let's define the angle as x degrees. The complement of the angle is therefore 90 - x degrees because the sum of an angle and its complement is 90 degrees. According to the problem statement, we can write the equation as follows:
x = 2(90 - x) - 141
Now, let's solve this equation step by step:
- Multiply out the bracket: x = 180 - 2x - 141.
- Combine like terms: x + 2x = 180 - 141.
- Simplify further: 3x = 39.
- Divide by 3 to find x: x = 13 degrees.
Therefore, the angle measurement is 13 degrees.