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)
To find the measures of the missing angles of the right triangle, we first need to calculate the value of x using the fact that the sum of the angles in a triangle is 180 degrees.
Let the acute angles of the right triangle be A, B, and C, where A and B are given as 2x + 6 and 3x - 26 degrees respectively. Since it is a right triangle, we know that the third angle (the right angle) is 90 degrees.
Using the Triangle Angle Sum Theorem: A + B + C = 180 degrees
(2x + 6) + (3x - 26) + 90 = 180
5x - 20 + 90 = 180
5x + 70 = 180
5x = 110
x = 22
Now that we have found the value of x, we can find the measures of the missing angles:
Angle A = 2x + 6 = 2(22) + 6 = 50 degrees
Angle B = 3x - 26 = 3(22) - 26 = 66 degrees
Therefore, the measures of the missing angles of the right triangle are:
Angle A = 50 degrees
Angle B = 66 degrees
Angle C (right angle) = 90 degrees.