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\:/(-1)}} \right.`
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`\left \{ {{\diagup\!\!\!\!x+y=90} \atop {-\diagup\!\!\!\!x+2y=-21}} \right.`
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`\left \{ {{y=90} \atop {2y=-21}} \right.`
------------------------------------

`3y = 69`

`y = (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`