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GI bisects LDGH so that mL DGI is x - 3 and mL ICH is 2x - 13. Find the value of x.
Since GI bisects LDGH, we know that mL DGI is equal to mL IGH. Therefore, we can set up the following equation:
x - 3 = 2x - 13
To solve for x, we can start by subtracting x from both sides of the equation:
-x + (x - 3) = -x + (2x - 13)
Simplifying, we have:
-3 = x - 13
Next, we can add 13 to both sides of the equation:
-3 + 13 = (x - 13) + 13
Simplifying further:
10 = x
Therefore, the value of x is 10.
To find the value of x, we can set the measures of the angles equal to each other since GI bisects LDGH.
mL DGI = mL ICH
x - 3 = 2x - 13 (Equating the measures of the angles)
To solve for x, we will isolate x on one side of the equation.
Subtract x from both sides:
x - x - 3 = 2x - x - 13
-3 = x - 13
Next, add 13 to both sides:
-3 + 13 = x - 13 + 13
10 = x
Therefore, the value of x is 10.