Explanation:
The sum of angles in ΔABD is ...
2a + b + d = 180
The sum of angles in ΔAHG is ...
a + h + 90 = 180
Solving this second equation for a, we have ...
a = 180 -90 -h = 90 -h
Substituting this into the first equation, we have ...
2(90 -h) +b +d = 180
180 -2h +b +d = 180 . . . . . eliminate parentheses
b + d = 2h . . . . . . . . . . . . . add 2h-180
h = (1/2)(b+d) . . . . . . . . . . divide by 2
