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) write this out and sound like a 7th grader
So, we have a right triangle with two acute angles. One angle measures 2x+6 degrees and the other angle measures 3x-26 degrees. We know that the sum of all the angles in a triangle is 180 degrees.
Since one angle is a right angle, it measures 90 degrees.
So, we can write an equation:
(2x+6) + (3x-26) + 90 = 180
Combine like terms:
5x - 20 + 90 = 180
5x + 70 = 180
Subtract 70 from both sides:
5x = 110
Divide by 5:
x = 22
Now, we can plug x back into the expressions for the acute angles:
2(22) + 6 = 50 degrees
3(22) - 26 = 40 degrees
So, the missing acute angles are 50 degrees and 40 degrees.