Since side HG is perpendicular to side HI, we know that angle G = angle I
We know that
G= (3x+26)°
I= (4x+14)°
Since G°=I°,
4x+14=3x+26
4x-3x=26-14
X= 12
Now, angle G=(3x+26)°
Since X=12,
G= (3(12)+26)°
G=62°
Since G=I, I would also be 62°
We know that all angles in a triangle must add up to 180°,
Therefore
angle H = 180-(2(62))
H= 180-124
H = 56°
And therefore we know that
Angle G = angle I = 62°
Angle H = 180-(Angle G + Angle I) = 56°