The measure of the supplement of an angle is 42 more than twice its complement. Find the original angle (to the nearest tenth if it is not a whole number).
To solve this problem, we need to understand the concepts of angles and their measures.
Let's start by defining the terms involved:
1. Complementary angles: Two angles are complementary if their sum is 90 degrees.
2. Supplementary angles: Two angles are supplementary if their sum is 180 degrees.
Now let's proceed with finding the original angle:
Let x be the original angle. According to the problem, we have two pieces of information:
1. The measure of the supplement of an angle is 42 more than twice its complement.
The complement of an angle is given by 90 - x.
Therefore, the supplement of the angle is 2(90 - x) + 42.
2. The sum of the angle and its supplement is 180 degrees.
So, we have x + (2(90 - x) + 42) = 180.
To solve for x, simplify the equation:
x + (180 - 2x + 42) = 180.
Combine like terms:
222 - x = 180.
Subtract 222 from both sides:
-x = -42.
Divide by -1:
x = 42.
Therefore, the original angle is 42 degrees.