In a right triangle, the measure of one acute angle is 12 more than twice the measure of the other acute angle. Find the measures of the 2 acute angles of the triangle. If the measures, in degrees, of the three angles of a triangle are x, , and , the triangle must be

Respuesta :

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.

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