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)
but make it a little short but that it shows the answer and that its not that smart
Using the Triangle Angle Sum Theorem, we know that the sum of the three angles in a triangle is 180 degrees.
So, we have:
2x + 6 + 3x - 26 + 90 = 180
5x + 70 = 180
5x = 110
x = 22
Therefore, the acute angles of the right triangle are:
2(22) + 6 = 50 degrees
3(22) - 26 = 40 degrees
Therefore, the measures of the missing angles are 90 degrees, 50 degrees, and 40 degrees.
how did u get that answer
I used the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is 180 degrees. By setting up an equation with the given angles in terms of x and solving for x, I found the value of x. Then, I substituted x back into the expressions for the acute angles to find their measures.
ok but solve it using the same method but in a different way
Let's denote the acute angles of the right triangle as A and B. According to the problem, we have:
A = 2x + 6
B = 3x - 26
By the Triangle Angle Sum Theorem, the sum of the angles must be 180 degrees:
A + B + 90 = 180
2x + 6 + 3x - 26 + 90 = 180
5x + 70 = 180
5x = 110
x = 22
Now, we can find the measures of angles A and B:
A = 2(22) + 6 = 50 degrees
B = 3(22) - 26 = 40 degrees
Therefore, the measures of the missing angles are 90 degrees, 50 degrees, and 40 degrees.