Question

find the measure of each angle acute angle in a right triangle where the measure of one acute angle is twice the difference of the measure of the other acute angle and 12​

Answer 1

Answer:

This is really just to help the other answer get brainiest because you cant have brainiest with only 1 answer.

Answer 2

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 $a$ and $b$.

$a + b +90 = 180$

The problem also says that one angle is twice the difference of the other angle and 12. That would look like this:

$a = 2(b-12)$

Now we have two equations. If we simplify them, we get these:

$\left \{ {{a=90-b} \atop {a=2b-24}} \right.$

Now you can substitute $a$ in the first equation for $a$ in the second equation

$90-b=2b-24$

Add $b$ to both sides of the equation

$90 = 3b-24$

Add $24$ to both sides

$114 = 3b$

Divide both sides by 3

$38 = b$

Now, you can substitute $38$ for $b$ in the first equation and simplify.

$a = 90-38$

$a=52$

Therefore,

$a=52$, and $b=38$

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