We know that the right triangle has one 90 degree angle and two acute (< 90 degree) angles. Since the sum of the angles of a triangle is always 180 degrees.
To find x:
(10x - 20) + (6x + 8) = 180
16x - 12 = 180
+12 +12
16x = 192
----- -----
16 16
x = 12
Check:
(10(12) - 20) + (6(12) + 8) = 180
(120 - 20) + (72 + 8) = 180
100 + 80 = 180
180 = 180
Angle (10x - 20):
(10(12) - 20)
(120 - 20)
100
Angle (6x + 8):
(6(12) + 8)
(72 + 8)
80