Explanation:
Let's represent the measure of the angle as x.
The complement of the angle is 90 - x degrees.
The supplement of the angle is 180 - x degrees.
According to the problem, the complement of the angle is 10° less than one-sixth of its supplement. This can be written as:
90 - x = (1/6)(180 - x) - 10
To solve for x, we need to simplify and solve the equation:
90 - x = (1/6)(180 - x) - 10
Multiply both sides of the equation by 6 to eliminate the fraction:
540 - 6x = 180 - x - 60
Combine like terms:
540 - 6x = 120 - x
Add 6x and x on both sides:
540 = 120 + 5x
Subtract 120 from both sides:
420 = 5x
Divide both sides by 5:
84 = x
Therefore, the measure of the angle is 84 degrees.