Two angles are complementary. the measure of one angle is 21 more than twice the measure of the other angle. find the measure of the angles

If x and y are the measures of the angles sought, from the task statement we can write the equations:

Data:
x + y = 90 (complementary)
x = 21 + 2y
 
Substituting the second equation in the first one, we have:

x + y = 90
21 + 2y + y = 90
3y = 90-21
3y = 69
y = 69/3
y = 23
 
Replace the value found, in the first equation, we will find the other angle:

x + y = 90
x + 23 = 90
x = 90-23
x = 67


The Angles → x = 67º and y = 23º

or

Data:
x + y = 90 (complementary) 
x = 21 + 2y → x - 2y = 21


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Now, Replace the value found, in the first equation, we will find the other angle: