To solve the problem, let’s denote the angle we are looking for as x.
The complementary angle of x is 90 – x.
According to the question, the angle x exceeds its complementary angle by 30 degrees. We can set up the equation:
x = (90 – x) + 30
Now, let’s simplify the equation:
x = 90 – x + 30
x + x = 120
2x = 120
x = 60
So, the angle that exceeds its complementary angle by 30 degrees is 60 degrees.
To verify, we can find the complementary angle:
The complementary angle of 60 degrees is 90 – 60 = 30 degrees.
Now, checking if the angle exceeds its complementary angle by 30 degrees:
60 – 30 = 30, which confirms our solution.
Thus, the angle we found is indeed correct.