Answer:
The measures of the acute angles are 38 and 52 degrees.
Step-by-step explanation:
In a right triangle, there are three angles, a right angle and two acute angles. In every traingle, the sum of the measures of the angles is 180 degrees. Let's call the acute angles [tex]a[/tex] and [tex]b[/tex].
[tex]a + b +90 = 180[/tex]
The problem also says that one angle is twice the difference of the other angle and 12. That would look like this:
[tex]a = 2(b-12)[/tex]
Now we have two equations. If we simplify them, we get these:
[tex]\left \{ {{a=90-b} \atop {a=2b-24}} \right.[/tex]
Now you can substitute [tex]a[/tex] in the first equation for [tex]a[/tex] in the second equation
[tex]90-b=2b-24[/tex]
Add [tex]b[/tex] to both sides of the equation
[tex]90 = 3b-24[/tex]
Add [tex]24[/tex] to both sides
[tex]114 = 3b[/tex]
Divide both sides by 3
[tex]38 = b[/tex]
Now, you can substitute [tex]38[/tex] for [tex]b[/tex] in the first equation and simplify.
[tex]a = 90-38[/tex]
[tex]a=52[/tex]
Therefore,
[tex]a=52[/tex], and [tex]b=38[/tex]
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