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
Answer:
The Angles → x = 67º and y = 23º
or
Data:
x + y = 90 (complementary)
x = 21 + 2y → x - 2y = 21
\(\left \{ {{x+y=90\:(I)} \atop {x-2y=21\:(II)}} \right.\)
------------------------------------
\(\left \{ {{x+y=90\:\:\:\:\:\:\:\:\:\:\:\:\:} \atop {x-2y=21\:\div(-1)}} \right.\)
------------------------------------
\(\left \{ {{\diagup\!\!\!\!x+y=90} \atop {-\diagup\!\!\!\!x+2y=-21}} \right.\)
------------------------------------
\(\left \{ {{y=90} \atop {2y=-21}} \right.\)
------------------------------------
\(3y = 69\)
\(y = \frac{69}{3}\)
\(\boxed{y = 23}\)
Now, Replace the value found, in the first equation, we will find the other angle:
\(x + y = 90\:(I)\)
\(x + 23 = 90\)
\(x = 90-23\)
\(\boxed{x = 67}\)
\(\underline{Answer:}\)
\(\boxed{\boxed{x= 67^0\:
y= 23^0}} \end{array}}\qquad\quad\checkmark\)
