The measure of angle HNS is 70°.
What is the measure of angle HNS?
Angle N = 180° - (20x - 35)° supplementary angles
= 180 - 20x + 35
Angle N = (215 - 20x)
Angle H = (12x - 16)°
Angle S = 40°
Angle H + Angle N + Angle S = 180° (sum of angles in a triangle)
12x - 16 + 215 - 20x + 40 = 180°
-8x + 239 = 180°
-8x = 180 - 239
-8x = -59
x = -59/-8
x = 7.25
Therefore,
Angle N = (215 - 20x)
= 215 - 20(7.25)
= 215 - 145
= 70°