Aright 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
The sum of the angles in a triangle is always 180 degrees.
So, we have:
(2x+6) + (3x-26) + C = 180
5x - 20 + C = 180
5x + C = 200
C = 200 - 5x
Since C is the third angle and it must also be an acute angle, it must be greater than 0. Therefore, we know that:
0 < 200 - 5x < 90
-200 < -5x < -110
40 > x > 22
Since x must be a whole number, the possible values for x are 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39.
Based on these possible values of x, we can find the measures of the missing angles:
When x = 23:
Angle 1 = 2(23) + 6 = 52 degrees
Angle 2 = 3(23) - 26 = 49 degrees
Angle 3 = 200 - 5(23) = 75 degrees
When x = 24:
Angle 1 = 2(24) + 6 = 54 degrees
Angle 2 = 3(24) - 26 = 50 degrees
Angle 3 = 200 - 5(24) = 80 degrees
And so on for the rest of the possible values of x.