In ΔGHI, \text{m}\angle G = (10x+9)^{\circ}m∠G=(10x+9)∘, \text{m}\angle H = (3x+13)^{\circ}m∠H=(3x+13)∘, and \text{m}\angle I = (x+4)^{\circ}m∠I=(x+4)∘. What is the value of x?x?

The angles in a triangle add up to 180.
The value of x is 14
Given that, GHI is a triangle.
It means that:
G + H + I = 180
So, we have:
10x + 9 + 3x + 13 + x + 4 = 180
Collect like terms
10x + 3x +x= 180 - 9 - 13 - 4
Evaluate the like terms
14x= 154
Divide through by 14
x = 11
Hence, the value of x is 14
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