A right triangle has acute angles measuring 2x+6

2

+
6
degrees and 3x−26
3


26
degrees. Use the Triangle Angle Sum Theorem to find the measures of the missing angles of the triangle.

1 answer

Given that the sum of all angles in a triangle is 180 degrees, we can set up an equation as follows:

(2x + 6) + (3x - 26) + (90) = 180

Combining like terms, we get:

5x - 20 = 180

Adding 20 to both sides:

5x = 200

Dividing by 5:

x = 40

Now we can find the measures of the missing angles by substituting x back into the expressions for the angles:

2x + 6 = 2(40) + 6 = 86 degrees
3x - 26 = 3(40) - 26 = 94 degrees

Therefore, the missing angles are 86 degrees and 94 degrees.