A right triangle has acute angles measuring 2x+6 degrees and 3x−26 degrees. Use the Triangle Angle Sum Theorem to find the measures of the missing angles of the triangle.(4 points)
in a short answer
To find the measures of the missing angles, we can use the Triangle Angle Sum Theorem, which states that the sum of the three angles in a triangle is always 180 degrees.
Let's call the missing angle of the triangle A. According to the Triangle Angle Sum Theorem, we have:
(2x + 6) + (3x - 26) + A = 180
Combining like terms, we get:
5x - 20 + A = 180
Subtracting -20 from both sides, we have:
5x + A = 200
Since we know that the triangle is a right triangle, one angle is 90 degrees. Therefore, we can rewrite the equation as:
5x + 90 = 200
Subtracting 90 from both sides, we get:
5x = 110
Dividing both sides by 5, we have:
x = 22
Now, we can substitute the value of x into the expressions for the acute angles:
2x + 6 = 2(22) + 6 = 44 + 6 = 50 degrees
3x - 26 = 3(22) - 26 = 66 - 26 = 40 degrees
Thus, the measures of the missing angles of the right triangle are 90 degrees, 50 degrees, and 40 degrees.