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.
could you simplify thisbut write it like a 12 year old but keep it formal
To find the missing angle, we use the fact that the three angles in a triangle add up to 180 degrees. Let's call the missing angle A. The equation becomes 5x + A = 200 because we know the triangle is a right triangle with a 90 degree angle.
As we solve the equation, we find that x is 22. Substituting x back into the expressions for the other angles, we get the missing angles are 50 degrees and 40 degrees.
Therefore, the missing angles in the right triangle are 90 degrees, 50 degrees, and 40 degrees.