Final answer:
The problem involves solving for an unknown angle using its relationship with its complement and supplement. By setting up an equation using this relationship and solving it, we find that the original angle is 42 degrees.
Step-by-step explanation:
The given problem falls under the category of angle relationships, specifically dealing with supplementary and complementary angles. Let's denote the unknown angle as 'x' degrees. The complement of an angle is what needs to be added to it to make 90 degrees, so the complement of our angle is (90 - x) degrees. Since 1/2 of the complement is said to be 1 degree more than 1/6 of the supplement, we can write this as an equation:
1/2 * (90 - x) = 1 + 1/6 * (180 - x)
Solving this equation will give us the value of the unknown angle 'x' which is our main goal.
We first expand both sides:
45 - 1/2x = 1 + 30 - 1/6x
Combining like terms gives us:
45 - 1/2x = 31 - 1/6x
Multiplying every term by 6 to eliminate the fractions, results in:
270 - 3x = 186 - x
Now, moving all the x terms to one side and the constants to the other, we have:
2x = 84
Dividing both sides by 2 to solve for x, we find that:
x = 42 degrees