Question

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

Answer 1

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,

$x+(2x+12)+90=180$

$3x+102=180$

$3x=180-102$

$3x=78$

Divide both sides by 3.

$x=\dfrac{78}{3}$

$x=26$

The measure of one acute angle is 26 degrees. So, the measure of another acute angle is:

$2x+12=2(26)+12$

$2x+12=52+12$

$2x+12=64$

Therefore, the measures of two acute angles are 26° and 64° respectively.