Bot. 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.
To find the missing angles of the triangle, we need to use the Triangle Angle Sum Theorem, which states that the sum of the interior angles of a triangle is always 180 degrees.
Let's denote the acute angles of the right triangle as A, B, and C. Since it is a right triangle, one of the angles is 90 degrees.
Given that angle A measures 2x + 6 degrees and angle B measures 3x - 26 degrees, the sum of the three angles of the triangle is:
90 + 2x + 6 + 3x - 26 = 180
96 + 5x - 20 = 180
5x + 76 = 180
5x = 180 - 76
5x = 104
x = 104 / 5
x = 20.8
Now, we can find the measures of angles A and B:
Angle A = 2(20.8) + 6
Angle A = 41.6 + 6
Angle A = 47.6 degrees
Angle B = 3(20.8) - 26
Angle B = 62.4 - 26
Angle B = 36.4 degrees
Therefore, the measures of the missing angles of the triangle are:
Angle A = 47.6 degrees
Angle B = 36.4 degrees