Question

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

Answer 1

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

$\left \{ {{x+y=90\:(I)} \atop {x-2y=21\:(II)}} \right.$
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$\left \{ {{x+y=90\:\:\:\:\:\:\:\:\:\:\:\:\:} \atop {x-2y=21\:\div(-1)}} \right.$
------------------------------------
$\left \{ {{\diagup\!\!\!\!x+y=90} \atop {-\diagup\!\!\!\!x+2y=-21}} \right.$
------------------------------------
$\left \{ {{y=90} \atop {2y=-21}} \right.$
------------------------------------
$3y = 69$
$y = \frac{69}{3}$
$\boxed{y = 23}$

Now, Replace the value found, in the first equation, we will find the other angle: 
$x + y = 90\:(I)$
$x + 23 = 90$
$x = 90-23$
$\boxed{x = 67}$

$\underline{Answer:}$

$\boxed{\boxed{x= 67^0\: y= 23^0}} \end{array}}\qquad\quad\checkmark$