Given:
In a right triangle, the measure of one acute angle is 12 more than twice the measure of the other acute angle.
To find:
The measures of the 2 acute angles of the triangle.
Solution:
Let x be the measure of one acute angle. Then the measure of another acute is (2x+12).
According to the angle sum property, the sum of all interior angles of a triangle is 180 degrees. So,
[tex]x+(2x+12)+90=180[/tex]
[tex]3x+102=180[/tex]
[tex]3x=180-102[/tex]
[tex]3x=78[/tex]
Divide both sides by 3.
[tex]x=\dfrac{78}{3}[/tex]
[tex]x=26[/tex]
The measure of one acute angle is 26 degrees. So, the measure of another acute angle is:
[tex]2x+12=2(26)+12[/tex]
[tex]2x+12=52+12[/tex]
[tex]2x+12=64[/tex]
Therefore, the measures of two acute angles are 26° and 64° respectively.