Final answer:
To find the angle, set up an equation using the complement and supplement of the angle and solve for 'x'.
Step-by-step explanation:
To solve this problem, let's first define the angle as 'x'. The complement of an angle is equal to 90 degrees minus the angle. So, the complement of 'x' is 90 - x. The supplement of an angle is equal to 180 degrees minus the angle. So, the supplement of 'x' is 180 - x.
According to the question, two-thirds of the complement of the angle is equal to 98 less than the supplement of the angle. Algebraically, this can be written as 2/3(90 - x) = (180 - x) - 98.
To solve this equation, we can simplify it by multiplying both sides by 3 to eliminate the fraction. This gives us: 2(90 - x) = 3((180 - x) - 98).
Now, we can distribute and solve for 'x'. After simplifying, we find that x = 34. Therefore, the angle is 34 degrees.