A right triangle has acute angles measuring 2x+6 degrees and 3x-26 degrees. Use the triangle angle sum theorem to find the measure of the missing angles of the triangle

1 answer

The sum of the measures of the angles in any triangle is always 180 degrees.

Let the missing angle be y degrees.

Therefore, we have the equation:

2x + 6 + 3x - 26 + y = 180

Combining like terms:

5x - 20 + y = 180

Rearranging the equation:

5x + y = 200

Since we know that x is a positive integer, we can find the possible values of x that make the equation true.

For x = 30:

5(30) + y = 200
150 + y = 200
y = 200 - 150
y = 50

Thus, the missing angle in the triangle is 50 degrees.