let 'x' and 'y' represent the angles

the sum of 2 angles id 204:

x + y = 204

one angle is 21 less then twice the other:

x = 2y - 21

by solving the system of equations we find:

x + y = 204

x = 2y - 21

we find:

x = 129 degrees

y = 75 degrees

click here to see the step by step solution of the system of equations:

the angles are 129 and 75 degrees.