What is m∠hlg?

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Since HLI and HLG are complementary angles (add together to make 90 degrees), you can set them up in the equation (25m + 22) + (9m) = 90.

25m + 22 + 9m = 90       add like numbers
34m + 22 = 90                subtraction property
34m = 68                        divide
m = 2

substitute m = 2 into the equation got angle HLG (25m + 22)

25(2) + 22
50 + 22
HLG = 72

So your equation is 

9m = 90 - 25m + 22

the reason is that ∠HLG = 9m
∠GLI = 90, meaning its a right angle

and ∠HLI = 25m +22

putting the equation together, than you just cancle it all out till all you have left is M then you multiply that by 9

i got m = 3 so 9*3 = 27